tag:blogger.com,1999:blog-7681481777504867762024-02-18T22:46:04.540-08:00Technomatics Engineering CompanyIn the business of Fluid Flow Engineering, Since 1992TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-768148177750486776.post-43696612200157322222014-08-18T03:03:00.000-07:002014-08-18T03:03:42.248-07:00Technical Presentation on Water Managment & Controls by TECHNOMATICS-DOROT at Goa<div dir="ltr" style="text-align: left;" trbidi="on">
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Invitation for Technical Presentation at GOA</div>
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Jointly organized by IWWA, Goa Chapter & Technomatics Engineering Company</div>
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Pictures of the event - 12.08.2014 at Country Inn & Suits, Patto Plaza, GOA </div>
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<br />Program attended by more than 100 engineers of PWD , JICA & PMC-JICA and Contractors from Goa. Thank you all.<br />
Our thanks to DOROT , Mr.Giora Heimann & Mr.Prasad Seth,Goa.<br />
<br /></div>
TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.com0tag:blogger.com,1999:blog-768148177750486776.post-24983423806190270142014-02-16T06:49:00.000-08:002014-02-16T09:49:28.542-08:00Comparison of Surge Protection Systems - HCV vs ZVV vs Surge vessel vs One way Surge tank<div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
<div align="center" class="MsoListParagraph" style="margin-left: 0cm; text-align: center;">
<span style="color: blue;"><b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="font-size: 14.0pt;">Comparison
of Surge Protection Systems-</span></u></b></span></div>
<span style="color: blue;">
</span><br />
<div align="center" class="MsoListParagraph" style="margin-left: 0cm; text-align: center;">
<span style="color: blue;"><b style="mso-bidi-font-weight: normal;"><u><span lang="EN-US" style="font-size: 14.0pt;">HCV
vs ZVV vs Surge vessel vs One way Surge tank</span></u></b></span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: #660000;"><b><i style="mso-bidi-font-style: normal;"><u>Definitions:</u></i></b></span></div>
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<i style="mso-bidi-font-style: normal;"><u><span style="text-decoration: none;"><br /></span></u></i></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: blue;"><b style="mso-bidi-font-weight: normal;">Hydraulic Check valve [HCV</b>]</span>
is an hydraulic valve, that closes in controlled pace when outlet pressure exceeds the inlet pressure (returning flow conditions). <span style="color: red;"><a href="https://www.blogger.com/null" name="OLE_LINK1"></a></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz350cCvJ5YD2ZjvRtJd9JVCD7kvDCGhZjc1ePedZg9BvHYT2P_wiSXNZqAclj-T2Fh94aHgrfTOiBJr23wuo-ZGLBa2ox-oZaLFcFEHOLDp3tWfYZkqMS3GSEUqvELvsnJGwmQgPEYyDd/s1600/SURGE+ANTICIPATING+VALVE.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz350cCvJ5YD2ZjvRtJd9JVCD7kvDCGhZjc1ePedZg9BvHYT2P_wiSXNZqAclj-T2Fh94aHgrfTOiBJr23wuo-ZGLBa2ox-oZaLFcFEHOLDp3tWfYZkqMS3GSEUqvELvsnJGwmQgPEYyDd/s1600/SURGE+ANTICIPATING+VALVE.JPG" height="240" width="320" /></a></div>
<div style="text-align: center;">
</div>
</div>
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<div style="text-align: center;">
<span style="color: blue;"><b style="mso-bidi-font-weight: normal;"><span style="color: black;">Installation of Surge Anticipating Valve</span> </b></span></div>
<br />
<span style="color: blue;"><b style="mso-bidi-font-weight: normal;">Zero-velocity check valve [ZVV]</b></span>
is a mechanical valve that closes very fast when outlet pressure exceeds the
inlet pressure (returning flow conditions).</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg041HdzIOQCLuN_XCnuUShedRhd3jHMbcMmnQF3P0g2IR_iu6SkGodHcuqgCWGBgAGYhCPtvlOIKPi3bQaC9fJX8OThmpYGfbrac_NM2dRSfSk4irwUxsdaHlNkMGJCZyeXCUZoSEJLDp_/s1600/ZVV.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg041HdzIOQCLuN_XCnuUShedRhd3jHMbcMmnQF3P0g2IR_iu6SkGodHcuqgCWGBgAGYhCPtvlOIKPi3bQaC9fJX8OThmpYGfbrac_NM2dRSfSk4irwUxsdaHlNkMGJCZyeXCUZoSEJLDp_/s1600/ZVV.JPG" height="213" width="320" /></a></div>
<div style="text-align: center;">
</div>
<div style="text-align: center;">
<b> Installation of Zero Velocity Valve</b></div>
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="color: blue;"><b style="mso-bidi-font-weight: normal;">Surge vessel</b></span> (Believe in this
case is a hydro-pneumatic tank) is a closed tank, that contains a specific
volume of water and the rest compressed air. It is located adjacent the surge-
generating device (pump, valve), connected to the main by suitable pipe, fills
the main by water on down-surge, and dissipates the kinetic energy of returning
flow by re-compressing the air.</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_9i8pRDKO21foDvvIMpJUazBLIekrvRsjnIxjMwvB43ljIySq3kO9FLk1fnVNclFEWQx1YfYt5rAYOLbL_jOWCuIQq17RDGx_zHsBsNN_JjZUrLsw5bv76PHNIQlTaYDM1Gi5uYCA4JtU/s1600/SURGE+VESSEL.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_9i8pRDKO21foDvvIMpJUazBLIekrvRsjnIxjMwvB43ljIySq3kO9FLk1fnVNclFEWQx1YfYt5rAYOLbL_jOWCuIQq17RDGx_zHsBsNN_JjZUrLsw5bv76PHNIQlTaYDM1Gi5uYCA4JtU/s1600/SURGE+VESSEL.JPG" height="240" width="320" /></a></div>
<div style="text-align: center;">
<b>Installation of Surge Vessel</b></div>
<div style="text-align: center;">
<br /></div>
</div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="color: blue;">One- way surge tank</span> </b>is an
open tank, which fills the main by water when the pressure in its location
falls below atmospheric value. It refilled gradually by water from the main
when the pressure rises, controlled by a float valve.</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;">
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSBTJYSm-GY50vNXpt6nkbOjfBLSsTB4jcC817f_yoAt2hahoqMHJlQAXLckMt-KrZKzCL1SxXFsSnrZAtZijWuiaHHVF0_imxH1LTuggAe0mxXOBsUsu6ePXXxdZkIoC1hZ3EvVonWjyH/s1600/ONE-WAY+SURGE+TANK.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSBTJYSm-GY50vNXpt6nkbOjfBLSsTB4jcC817f_yoAt2hahoqMHJlQAXLckMt-KrZKzCL1SxXFsSnrZAtZijWuiaHHVF0_imxH1LTuggAe0mxXOBsUsu6ePXXxdZkIoC1hZ3EvVonWjyH/s1600/ONE-WAY+SURGE+TANK.JPG" height="213" width="320" /></a></div>
<div style="text-align: center;">
<b>Installation of One Way Surge Tank</b></div>
<div style="text-align: center;">
<br /></div>
</div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;">
<i style="mso-bidi-font-style: normal;"><u><b><span style="color: #660000;">Relevant comparisons: HCV and ZVV, Surge
vessel and one-way tank :</span></b></u></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="color: blue;">HCV vs ZVV</span>: </b>Water hammer is
result of velocity change: kinetic energy of the water mass converted to
pressure when the water decelerates or accelerates. The time of change is a
very important factor: increasing the pace of the change reduces the magnitude
of pressure spike.</div>
<ul style="text-align: left;">
<li><span lang="EN-US" style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US">HCV closes slowly, hence
reduces the water hammer potential.</span></li>
</ul>
</div>
<ul style="text-align: left;">
<li><span lang="EN-US" style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US">ZVV closes very fast, before
the returning flow accelerates, so the velocity change is minor.</span><span lang="EN-US" style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"> <span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US"> </span></li>
</ul>
<span lang="EN-US"> Hence the solution provided by
the two is entirely different and the efficiency depends on the conditions of
the specific case.</span><br />
<div>
<ul style="text-align: left;">
<li><span lang="EN-US" style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-US">HCV allows returning flow for
considerable period- that causes backward-rotation of the pump. Not possible
when the suction is negative (above-water pump) as it applies the pressure on
the foot valve.</span></li>
</ul>
<ul style="text-align: left;">
<li><span lang="EN-US" style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US">ZVV may generate high water
hammer if located incorrectly in the middle of the pipe, is an inline device
that cannot be inspected or tested, may generate cavitation conditions and
pipe-collapse if not accompanied by suitable air valves.</span></li>
</ul>
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US">Both create certain head loss
and energy waste.</span></div>
<div class="MsoListParagraph">
<br /></div>
<div class="MsoNormal">
<span style="color: blue;"><b><span style="mso-bidi-font-weight: normal;">Closed
hydro-pneumatic</span> tank</b></span> is a very good solution for transient conditions, as
it is practically an energy storage that is activated automatically when the
pump energy is gone, and dissipates kinetic energy of decelerated water mass.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="color: blue;"><b style="mso-bidi-font-weight: normal;">Open tank</b></span> can be
used only to prevent column separation by inserting water to the pipe in its
location. It can replace air valve- but it can not prevent pressure spike
caused by returning flow. Normally used in the peaks along the main.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Both are relatively-expensive solution; require professional
maintenance, freshening of the water volume, special control valves. Closed
tank requires also compressor[s] and sophisticated water-level control. The
sizing of both types is a critical factor, as too-small tanks will not provide
the expected results. Both cannot be inspected without simulation of the
water-hammer, meaning stop of the pumping.</div>
<div class="MsoNormal" style="text-align: center;">
***** </div>
</div>
</div>
TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.com0tag:blogger.com,1999:blog-768148177750486776.post-640648037644366912014-02-13T21:13:00.000-08:002014-02-13T21:13:09.805-08:00Suction Specific Speed of Impeller Pumps<div dir="ltr" style="text-align: left;" trbidi="on">
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<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Suction Specific
Speed</span></h2>
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<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Definition of Suction Specific
Speed</span></h4>
<em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Suction specific speed</span></em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">, like specific speed, is not a speed at all.
It is an index number, or "yardstick." It is based on the NPSHR of a
centrifugal pump, normally the 3 percent head drop NPSHR and normally at its
best efficiency point (BEP). The equation for suction specific speed is the
same as specific speed, except that NPSHR is substituted for head, as follows:</span><br />
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<![endif]--><span lang="EN-US" style="font-family: "Cambria","serif"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-hansi-theme-font: major-latin;"></span>
(13-2)</span><br />
<br />
<div style="margin-bottom: .0001pt; margin-bottom: 0cm;">
<em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Where (in U.S. units):</span></em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">S
= Suction Specific Speed</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">N
= RPM of Pump</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Q
= Pump Capacity*†, GPM</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">NPSHR
= NPSH required by pump†, feet</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">*If the impeller is double suction, Q in the
above equation is one-half the BEP capacity of the pump. This is a major
difference from calculating specific speed, in which we use total pump
capacity, whether the impeller is single suction or double suction.</span></em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span></div>
<em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">†Normally calculated at the BEP</span></em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">The symbol Nss is often used in
place of S for suction specific speed.</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">The value of S for most pumps is
typically between 7,000 and 15,000. The higher values are more common in higher
speed, higher capacity units. (See next month's article for additional
discussion of the effect of speed and capacity on S.)</span><br />
<h5>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Problem No. 1: Suction Specific
Speed</span></h5>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Calculate the suction specific
speed for the pump represented by the performance curve in Figure A (Figure 2
from the May column).</span><br />
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">N
= 3,550 rpm</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Q<sub>bep</sub>
= 450 gpm</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">NPSHR<sub>bep</sub>
= 14 ft</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">S
= <img alt="Suction Specific Speed Equation to Solve Problem 1" height="49" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.jpg" width="89" />=
<img alt="Suction Specific Speed Equation Problem 1" height="49" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.jpg" width="77" />=10,400
(RPM-GPM-FT)10,400 (RPM‑GPM‑FT)</span></div>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">(Our answer is different than the
9,000 stated on the curve.)</span><br />
<br />
<div align="center" style="text-align: center;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><img alt="Figure A. Typical published performance curve. Single-line NPSH curve." height="273" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image004.jpg" width="365" /></span></div>
<strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Figure A. Typical published performance
curve. Single-line NPSH curve.</span></strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span><br />
<h4>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Importance of Suction Specific
Speed</span></h4>
<em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Establishing a Maximum Value for
S</span></em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">For a number of years, the push
from users and competitors required pump manufacturers to continually strive
for lower values of NPSHR. The philosophy was that "The lower the NPSHR,
the better the pump." (NPSHR in centrifugal pumps is normally reduced by
increasing the diameter of the impeller eye, as shown in Figure 1.) That
philosophy has now changed. Due to problems that have been attributed to
oversized impeller eyes, pump users have established maximum values for S,
which establishes minimum values for NPSHR.</span><br />
<br />
<div align="center" style="text-align: center;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><img alt="Figure 1. To reduce NPSHR, the impeller eye diameter is increased." height="210" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image006.jpg" width="375" /></span></div>
<strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Figure 1. To reduce NPSHR, the
impeller eye diameter is increased.</span></strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span><br />
<em><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Establishing a "Stable"
Window of Operation</span></em><br />
<br />
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Every
centrifugal pump would like to run at its BEP-always. All pump components would
experience maximum life at that capacity.</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Seldom
does a pump run at its BEP, but component life will be significantly extended
if it operates within its "stable" window of capacities.</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">To
a large extent, suction specific speed indicates the size of that window. Pumps
with lower values of S have larger windows.</span></div>
<div style="margin-bottom: .0001pt; margin: 0cm;">
<br /></div>
<h4 style="margin-bottom: .0001pt; margin: 0cm;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Suction
Recirculation, or the "Big Eye Syndrome" (Monster or Myth?)</span></h4>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">For decades, industry recognized
that centrifugal compressors would "surge" if operated below a
certain capacity, but only more recently have we recognized that centrifugal
pumps have a comparable characteristic.</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">We now know that any centrifugal
pump will experience <em><span style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">recirculation </span></em>in the
impeller eye if the capacity is below a certain value. Larger impeller eyes and
higher speeds (i.e., higher peripheral velocity of the eye-U<sub>1</sub>)
produce higher energy recirculation.</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">The large eye required to obtain
low NPSHR leads to the problem of (higher energy) "eye recirculation"
or "suction recirculation" (4). As shown in Figure 2, flow through
the eye is proper at the BEP, but at some reduced capacity, recirculation
starts in the large eye. As pump capacity is further reduced, the intensity of
the circulation increases, sometimes resulting in a reversal of flow at the
i.d. of the suction pipe, near the pump. If strong enough, this vortex causes
cavitation, noise and pulsations. The capacity, at which this recirculation
starts, increases as the eye diameter is increased.</span><br />
<br />
<div align="center" style="text-align: center;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><img alt="Figure 2. Although resulting in reduced NPHR at the BEP, the large eye creates eddies and recirculation at reduced flow rates." height="184" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image007.jpg" width="445" /></span></div>
<strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Figure 2. Although resulting in
reduced NPHR at the BEP, the large eye creates eddies and recirculation at
reduced flow rates.</span></strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">When the vortices are strong
enough to cause cavitation, the vapor bubbles collapse on the <em><span style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">driving</span></em> side, or pressure side,
of the impeller vane, near the eye. If the vane twists as it enters the eye
from the larger diameter, this part of the vane cannot be seen by looking
directly into the eye, but must be viewed with the assistance of a small
mirror.</span><br />
<h4>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Study by Hallam</span></h4>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Numerous technical papers and
articles reported problems caused by suction recirculation, but none quantified
the phenomenon until Hallam (5) reported in 1982 the results of a 5 year study
of 480 centrifugal pumps in Amoco's Texas
City refinery. Most of these pumps were in hydrocarbon
services. The remainder pumped water. The average power requirement was about
150 hp and the maximum was 1,000 hp.</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Figure 3 shows the results of the
study. The pumps were divided in groups according to their suction specific
speed. The average numbers of failures/year/pump were plotted for each group. A
failure was defined as any problem with the pump that required service in the
refinery repair shop. The graph shows an increase in failure frequency of
almost 100 percent above an S of about 11,000.</span><br />
<br />
<div align="center" style="text-align: center;">
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"><img alt="Figure 3. Failure frequency vs. suction specific speed (J.L. Hallam, [5])" height="209" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image008.jpg" width="400" /></span></div>
<strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Figure 3. Failure frequency vs.
suction specific speed (J.L. Hallam, [5])</span></strong><br />
<br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">The logic contained in some of
the papers on suction recirculation is not totally rigorous. Most of the
symptoms attributed to recirculation can be attributed to other centrifugal
pump phenomena. The high S attributed to some centrifugal pumps has also been
found to have been obtained by improper methods of NPSH testing. Ross (6)
claims that the problem of suction recirculation has been distorted-that it
simply boils down to inadequate NPSHA.</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Regardless of the reason for the
problem-whether it is suction recirculation, improper methods of testing or
just inadequate NPSHA-Hallam's paper clearly shows that a pump with a suction
specific speed greater than 11,000 should be selected with caution.</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">This finding caused a number of
companies to prohibit the purchase of a pump with a suction specific speed in
excess of 11,000.</span><br />
<h5>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Problem No. 2. Suction Specific
Speed for a High Speed Multistage Waterflood Pump</span></h5>
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">A four-stage pump is operating on
an offshore platform in waterflooding (secondary recovery) service. Figure 4 is
a redrawn copy of the performance curve provided by the pump manufacturer. The
pump is equipped with a double suction, first stage impeller.</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Calculate the suction specific
speed:</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">S = <img alt="Suction Specific Equation to Solve Problem 2" height="49" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.jpg" width="89" />=<img alt="Problem No. 2: Suction Specific Speed for a High Speed Multistage Waterflood Pump" height="49" src="file:///C:\Users\RAVICH~1\AppData\Local\Temp\msohtmlclip1\01\clip_image009.jpg" width="81" />= 12,000 (RPM-GPM-FT)</span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Would you suspect that this pump
could be a problem? Yes, and it was. </span><br />
<span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">The first stage impeller would
periodically experience cavitation-erosion on the pressure side of the vanes,
throwing the rotor out of balance and causing excessive vibration.</span><br />
<br />
<div align="center" style="text-align: center;">
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<strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;">Figure 4. The vendor performance
curve for the water flood pump</span></strong><span lang="EN-US" style="font-family: "Cambria","serif"; mso-ascii-theme-font: major-latin; mso-hansi-theme-font: major-latin;"></span><br />
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TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.com0tag:blogger.com,1999:blog-768148177750486776.post-36161568943192006692014-02-13T20:34:00.000-08:002014-02-13T20:34:55.323-08:00Comparision of Surge Systems<div dir="ltr" style="text-align: left;" trbidi="on">
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</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Requires design of proper air valves and/or
one-way filling tanks.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Very large capacity may be required for the
pipe filling stage and local high points.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Accessories</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Does not require any external additions except
a drain pipe to the sump.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Requires compressor, backup compressor &
sophisticated control systems to maintain the proper water volume in the tank</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Check valve</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">slam</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Prevents mechanical slam to the check valve.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Increases mechanical slamming to the check
valve.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4;">
<td rowspan="2" style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">System Cost</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Low-cost for larger systems - valve size is
reduced, mostly, as the pipe is longer. (longer pipes have a higher friction,
and returning flow is smaller)</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Very high cost for large systems. The tank size
increases with capacity of the pipe, so longer pipes require larger vessels</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 5;">
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Expensive, not practical for small networks (up
to 8")</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Low cost for small system protection</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 6;">
<td style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Maintenance</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Low-cost and easy maintenance - only periodical
testing required.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">High maintenance costs: Compressor, control
system and micro-crack detection</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 7;">
<td style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Testing</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Enables periodical operation tests
without stop of pumping.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Does not allow a test without completely stop
of pumping.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 8;">
<td style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Footprint</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Requires minimal space</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Requires large space</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 9;">
<td style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Relief function</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;"> High Pressure Relief function is added as
a standard feature of the valve</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Not included, cannot prevent abnormal high
pressure in the network during pumping</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 10; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 104.65pt;" valign="top" width="140"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Protection of raw-water & sewage system</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 276.4pt;" valign="top" width="369"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Included in the standard valve. Same
protection. No additional parts. Clean or filtered media is required.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; padding: 0cm 5.4pt 0cm 5.4pt; width: 233.9pt;" valign="top" width="312"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Makes the maintenance even more difficult &
expensive task. Not recommended.</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-indent: -14.2pt;">
<b><u><span lang="EN-US" style="color: #5e5e5e; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Summary</span></u></b><span lang="EN-US" style="color: #5e5e5e; font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="color: #5e5e5e; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Though air-vessels are the most
common method of surge-protection used nowadays in design of pumping system, it
is our opinion that using Surge-Anticipating Valves should be seriously considered due to its low cost, ease of maintenance (cost of
ownership) and reliability.</span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span lang="EN-US" style="color: #5e5e5e; font-size: 12.0pt; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Combination of Air Release Valves
with Surge-Anticipating valves, if properly sized and adjusted, will supply an
equal level of protection for large systems, at a much lower cost and smaller
footprint.</span></div>
<div class="MsoNormal" style="background: white; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<br />
<div class="MsoNormal" style="background: none repeat scroll 0% 0% white; line-height: normal; margin-bottom: 0.0001pt; text-align: left;">
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TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.com0tag:blogger.com,1999:blog-768148177750486776.post-20037796211650694802014-02-11T23:43:00.000-08:002014-02-11T23:43:19.607-08:00Pipe Stress- Hoop, Longitudinal & Radial <div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="color: blue;"><u><b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman"; mso-font-kerning: 18.0pt;">Induced
Stresses in Pipe- Hoop, Longitudinal and Radial Stresses</span></b></u></span></div>
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<b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Introduction to Induced Stresses:</ins></span></span></b></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>When the
ends of the pipe ends are closed and pipe is subjected to an internal <b>pressure
‘P’ </b>there are various stresses that develop in the pipe. Each element of
pipe are subjected to the below mentioned stresses which act in the direction
as shown in the fig.1.</ins></span></span></div>
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<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Circumferential (hoop) stress </ins></span></span><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>H</ins></span></span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Longitudinal Stress </ins></span></span><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>L</ins></span></span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Radial Stress </ins></span></span><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>R</ins></span></span></li>
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" /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Fig 1:
Different stresses induced in pipe</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 2;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 2;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>CIRCUMFERENTIAL OR HOOP STRESS: </ins></span></span></b><b><span style="font-family: Symbol; font-size: 16.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>H </ins></span></span></b></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>The effect
of this may split the pipe into two halves as shown in fig.2. The failure of
the pipe in two halves in fact is possible across any plane, which contains
diameter and axis of the pipe. Elements resisting this type of failure would be
subjected to stress and direction of this stress is along the circumference. Hence
the above stress is called <b>Circumferential or Hoop Stress.</b></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>If -</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>D </ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>= Diameter of the pipe</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>L </ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>= Length of the pipe</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>t </ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>= thickness of the pipe.</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Then</ins></span></span></div>
<table border="0" cellpadding="0" class="MsoNormalTable" style="mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Bursting force, FB</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Pressure * Area</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<br /></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">P * D * L</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> Resisting force, F<sub>R</sub>
</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Resisting metal area * Stress, </span></b><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">H </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td colspan="3" style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Equating <b>F<sub>B</sub> & F<sub>R</sub></b></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> P * D * L </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">2t * L * </span></b><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">H</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 5;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><b><span style="font-family: "Cambria Math","serif"; font-size: 12.0pt; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Times New Roman";">∴</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> t</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">(P * D)/ 2 * </span></b><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">H </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 6; mso-yfti-lastrow: yes;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> or
</span></b><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">H
</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">(P * D) /( 2 * t)
______________________(1) </span></b><b><span style="font-family: "Georgia","serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">
</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>This
equation is used for calculating the thickness of pipe so as to withstand
pressure <b>‘P’ </b>where </ins></span></span><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins> <b>H </b>is <b>allowable
circumferential stress.</b></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins><br /></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<img alt="" 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" /><br /><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-no-proof: yes;"></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins><br /></ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-no-proof: yes;"></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Fig 2:
Circumferential or Hoop stress</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 2;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>LONGITUDINAL STRESS:</ins></span></span></b><b><span style="font-family: Symbol; font-size: 16.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>R</ins></span></span></b></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Considering
that the pipe ends are closed and pipe is subjected to <b>an internal pressure
‘P’ </b>the pipe may fail as shown in <b>Fig.3</b>. Elements resisting this
type of failure would be subjected to stress and direction of this stress is
parallel to the longitudinal direction of the pipe. Hence this stress is called
<b>longitudinal stress</b>.</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Then</ins></span></span></div>
<table border="0" cellpadding="0" class="MsoNormalTable" style="mso-cellspacing: 1.5pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Bursting force, FB
</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Pressure </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">× <b>Area
</b></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 1;">
<td style="padding: .75pt .75pt .75pt .75pt;"><br /></td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">P *</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> (<b>πD * D)/4</b></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 2;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Resisting force,
FR </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Resisting metal area</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> <b>x</b> <b>Stress, </b></span><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">L</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 3;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">π D t * </span></b><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">L </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">(when <b>t
</b>is significantly small as compared to <b>D</b>)</span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 4;">
<td colspan="3" style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Equating <b>F<sub>B</sub> & F<sub>R</sub></b></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 5;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">P * (<u>π</u>D * D) /4</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">π D t * </span></b><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">L </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 6;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Cambria Math","serif"; font-size: 12.0pt; mso-bidi-font-family: "Cambria Math"; mso-fareast-font-family: "Times New Roman";">∴</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> <b>t
</b></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><u><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">(P D)/</span></u></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">4 * </span></b><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">L</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
<tr style="mso-yfti-irow: 7; mso-yfti-lastrow: yes;">
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">or </span><b><span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">s</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">L </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">=</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
<td style="padding: .75pt .75pt .75pt .75pt;">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><u><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">(P D)/(4 * t)</span></u></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">
_________________________ (2)</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>NOTES: </ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-margin-top-alt: auto;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>1)
</ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>On comparing
equations <b>1 & 2</b>, it is clear that when a pipe having diameter <b>‘D’
</b>and thickness <b>‘t’ </b>is subjected to an internal pressure <b>‘P’, </b>the
induced circumferential tress is double the induced longitudinal stress.</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>2)
</ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Normally,
the pipe is considered as a thin wall cylinder i.e. <b>t </b>< <b>D/6 </b></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>3)
</ins></span></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Usually <b>D
</b>is substituted by <b>Do </b>(outside diameter) in order to have higher
safely margin.</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins><br /></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<img alt="" src="data:image/png;base64,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" /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-no-proof: yes;"><br /></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Fig 3:
Longitudinal stress</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins> </ins></span></span><b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>RADIAL STRESS: </ins></span></span></b><b><span style="font-family: Symbol; font-size: 16.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 16.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>R </ins></span></span></b></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Radial
stress is a stress in directions coplanar with but perpendicular to the
symmetry axis.</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>The radial
stress for a thick-walled <a href="http://en.wikipedia.org/wiki/Cylinder_%28engine%29" title="Cylinder (engine)"><span style="color: windowtext;">pipe</span></a> is
equal and opposite to the gauge pressure on the inside surface, and zero on the
outside surface.</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>The radial
stress is always compressive.</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Each element
of the pipe is subjected to radial stress which acts in radial direction as
shown in <b>Fig.4</b> and calculated as</ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: Symbol; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>s</ins></span></span><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>R
= P</ins></span></span></b></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins><br /></ins></span></span></div>
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<img alt="" 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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-no-proof: yes;"><br /></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins></ins></span></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span class="msoIns"><ins>Fig 4:
Radial stress</ins></span></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">*****</span></div>
<div class="MsoNormal" style="text-align: right;">
<br /></div>
<div class="MsoNormal" style="text-align: right;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">Source: http://www.piping-engineering.com</span></div>
</div>
TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.com0tag:blogger.com,1999:blog-768148177750486776.post-54377468590088857952014-01-14T19:14:00.001-08:002014-01-14T21:58:28.093-08:00Surge Pressure | Water Hammer <div dir="ltr" style="text-align: left;" trbidi="on">
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<u><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">SURGE PRESSURE or WATER HAMMER</span></u></h1>
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<![endif]--><span lang="EN-US" style="color: black; font-family: "Cambria","serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-latin; mso-bidi-font-family: Helvetica; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-latin;">Surge or water hammer, as
it is commonly known is the result of a sudden change in liquid velocity. Water
hammer usually occurs when a transfer system is quickly started, stopped or is
forced to make a rapid change in direction. Any of these events can lead to
catastrophic system component failure.</span><br />
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">The objective for a
water hammer investigation should be to suppress transient pressures to
acceptable limit and avoid the following:</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Pipeline
bursts and leaks</span></b><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">. </span></div>
<ul style="text-align: left;">
<li><span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Positive water hammer pressures should be
limited to the pipe acceptable working pressure. It is not uncommon in plastic
pipes, such as polyethylene to add 25% to the allowable working pressure
because these materials are stronger and stiffer under rapid loading rates
(e.g. transient loading conditions) than they are under lower loading rates. </span></li>
<li><span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Pipelines can fail by buckling resulting from
excessive vacuum during transient conditions in the case of thin walled large
diameter steel pipe, low pressure rating plastic pipe and plastic pipes exposed
to high temperatures. </span></li>
<li><span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Cement lining in steel pipes has spelled off
the pipeline in situations where the pipeline is subjected to vacuum conditions
accompanied by large pressure fluctuations. The exposed metal surface corrodes
resulting in accelerated pipeline failure. </span></li>
<li><span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;"><span style="font: 7.0pt "Times New Roman";"></span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Asbestos Cement rubber ring joints have
failed from vacuum pressures resulting from pump stoppages. The vacuum
pressures have allowed air to enter the pipeline via the rubber ring joints and
the joints have failed with time exposure. </span></li>
</ul>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Damaged Equipment</span></h1>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l0 level1 lfo4; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">This may occur due to the violent movement of
mechanical parts. Examples of these are check valves slamming shut following
pump stoppages at multiple pump stations and the sudden closure of large
orifice air valves when filling pipelines. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">BASIC UNDERSTANDING</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">The magnitude of a
pressure change under a transient condition is expressed by Joukowsky’s law for
instantaneous valve closure: </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 36.0pt; text-align: justify;">
<span lang="EN-US" style="font-family: "Lucida Sans Unicode","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: Arial;">△</span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;"> h(max)<span style="mso-spacerun: yes;">
</span>=<span style="mso-spacerun: yes;"> </span><u>a<span style="mso-spacerun: yes;"> </span>Vo</u></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span><span style="mso-spacerun: yes;"> </span>g</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;"><span style="mso-tab-count: 2;"> </span>where <span style="mso-tab-count: 1;"> </span></span><span lang="EN-US" style="font-family: "Lucida Sans Unicode","sans-serif"; font-size: 10.0pt; mso-bidi-font-family: Arial;">△</span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">
h(max)<span style="mso-tab-count: 1;"> </span>= <span style="mso-tab-count: 1;"> </span>change in pressure in meter head</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;"><span style="mso-tab-count: 6;"> </span></span></div>
<div class="MsoBodyTextIndent" style="text-align: justify;">
<span lang="EN-GB" style="font-family: "Arial","sans-serif";">a<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>celerity or the speed of the surge
wave </span></div>
<div class="MsoBodyTextIndent" style="text-align: justify;">
<span lang="EN-GB" style="font-family: "Arial","sans-serif";"><span style="mso-tab-count: 2;"> </span>through
the liquid in the pipeline in m/s</span></div>
<div class="MsoBodyTextIndent" style="text-align: justify;">
<span lang="EN-GB" style="font-family: "Arial","sans-serif";">Vo<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>change in velocity m/s</span></div>
<div class="MsoBodyTextIndent" style="text-align: justify;">
<span lang="EN-GB" style="font-family: "Arial","sans-serif";">g<span style="mso-tab-count: 1;"> </span>=<span style="mso-tab-count: 1;"> </span>acceleration due to gravity as 9.8
m/s²</span></div>
<div class="MsoBodyTextIndent" style="text-align: justify;">
<span lang="EN-GB" style="font-family: "Arial","sans-serif";"><span style="mso-spacerun: yes;">
</span><span style="mso-tab-count: 3;"> </span></span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">The formula provides
an initial first step guide as to what likely pressures could be developed
during a transient condition. It also demonstrates the impact of different pipe
materials.Steel pipe has celerity of 1000 m/s compared to 250 m/s for
polyethylene pipe. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">The sudden closing of
a valve with a pipe flow velocity of 1.0 m/s would generate a pressure change
of 100 m head in the steel pipe compared to 25 m head in the polyethylene. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">The use of a water
hammer program is recommended for determining likely pressure surges even in
simple piping system. There are many factors that influence transient pressure
surges, they include:</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Pipeline profile (particularly high points)</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Pipeline anchorage </span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Type of pipe material (and presence of
linings)</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Location of storage’s</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Type of check valves (some are vulnerable to
valve slamming)</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Pump performance curves and operating speeds</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Rotational moment of inertia’s for pump/motor
assemblies</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Pump station configurations</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Location and type of air valves</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Protection devices installed</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Configuration of piping network</span></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l2 level1 lfo3; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: Symbol; font-size: 10.0pt; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Valve types, sizes and their opening/closing
speed</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">A very effective method
to visually demonstrate water hammer in a system is to use animation
enhancement. The animation program shows a time-based simulation of the
changing hydraulic levels and velocity profiles changing along the pipeline
profile during a transient condition. It shows the interaction between the traveling
pressure surge wave, changing hydraulic level and velocity profiles and the
impact of boundary conditions such as storage tanks, check valve, pumps,
changes in pipe diameter, etc. The program is particularly useful when
demonstrating water hammer to personnel with limited experience in the subject.
</span></div>
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<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">PROTECTION DEVICES</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Every water supply
system is unique in relation to water hammer effects. The most effective
solution to a potential water hammer problem may be a single or combination of
protection devices. The relative merits of various devices should be compared
and the best solution evaluated during the design phase of a new project. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">A number of commonly
used protection devices are described:</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Flywheel</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">An effective device
attached to pumps for generally shorter pipeline lengths. They help to dampen
surges by slowly decelerating the pump speed on pump stoppage. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Air Vessel</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">A pressure vessel
containing air and water. It is a very effective device for controlling both
positive and negative pressure surges and is often used as a last resort
because of high capital costs. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">One Way Surge Tower</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">An open ended device
which is connected to the pipeline by a check valve. It allows water to enter
the pipeline when the pipeline is subjected to vacuum pressures. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Non Return Valves</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">These are often used
on steeply rising pumping mains. They help to prevent the pipeline length of
water falling back on the pump’s check valve following pump stoppage.</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Standpipe</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Can be used in low
pumping head systems where the height of the standpipe does not become
excessive. They are often used on gravity systems.</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Control Valves</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">They are often fitted
on pump discharges. They are opened and closed slowly to minimize water during
pump stoppage and startup. They are not effective during a sudden pump
stoppage. </span></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">Surge Anticipator Valves</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">They are fitted to a
pump delivery. They are hydraulically activated control valves which open when
a pump stops and start to close as the pressure starts to build up when down
surge reaches the pump. The slow closure of the valve minimizes water hammer
pressures. </span></div>
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<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<h1 style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">CONCLUSION</span></h1>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">The difficulty in
understanding the process of water hammer has given rise to certain
misconceptions:</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l1 level1 lfo1; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">pipeline velocities must be low to reduce the
effects of water hammer</span></div>
<div class="MsoNormal" style="text-align: justify; text-indent: 3.0pt;">
<br /></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l1 level1 lfo1; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">surges only occur in long pipelines</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l1 level1 lfo1; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">the noise and knock in a system is an
indicator of the magnitude of a surge </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l1 level1 lfo1; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">surge protection devices should be installed
on an experimental basis because it is not possible to accurately determine the
magnitude of surges</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l1 level1 lfo1; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">the use of surge protection devices are not
economically viable</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="margin-left: 18.0pt; mso-list: l1 level1 lfo1; tab-stops: list 18.0pt; text-align: justify; text-indent: -18.0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt; mso-fareast-font-family: Arial;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">pressures in a system must be high before
dangerous surges can occur</span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10.0pt;">A water hammer
investigation should be an integral part during the design phase for a new
project, and if potential water hammer problems are identified, then the most
effective selection of protection devices should be installed for that system. </span></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
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<div class="MsoNormal">
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TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.com0tag:blogger.com,1999:blog-768148177750486776.post-32490626061083719722014-01-14T10:57:00.000-08:002014-01-14T10:57:10.816-08:00Technomatics Catalogue<div dir="ltr" style="text-align: left;" trbidi="on">
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TECHNOMATICShttp://www.blogger.com/profile/10405349183639941449noreply@blogger.com0