Laws of Affinity

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0 height="100%"><tr> <td valign="top" width=200 BGCOLOR="#003333" TEXT="#F7F7FF" background="133d8c00dduajq.jpg"> <bR> <bR> <div> <A HREF="index.htm" TARGET="_top" TITLE="HughesPrimeau Controls, Inc."><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Home</B></U></A></div> <div> <A HREF="id2.htm" TARGET="_top" TITLE="About Us"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">About Us</B></U></A></div> <div> <A HREF="id3.htm" TARGET="_top" TITLE="Products and Services"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Products and Services</B></U></A></div> <div> <A HREF="hughes_primeau_controls_line_card.htm" TARGET="_top" TITLE="Product Line Card"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Product Line Card</B></U></A></div> <div> <A HREF="id52.htm" TARGET="_top" TITLE="Product Announcements"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Product Announcements</B></U></A></div> <div> <A HREF="id63.htm" TARGET="_top" TITLE="Cool Orders of the Week"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Cool Orders of the Week</B></U></A></div> <div> <A HREF="id20.htm" TARGET="_top" TITLE="Henry Hughes"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Henry Hughes</B></U></A></div> <div> <A HREF="id55.htm" TARGET="_top" TITLE="HPC Mission Statement"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">HPC Mission Statement</B></U></A></div> <div> <A HREF="id4.htm" TARGET="_top" TITLE="Request for More Information or a Quote"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Request for More Information or a Quote</B></U></A></div> <div> <A HREF="id6.htm" TARGET="_top" TITLE="Map to our Office"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Map to our Office</B></U></A></div> <div> <A HREF="id70.htm" TARGET="_top" TITLE="Cool Pictures of HPC"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Cool Pictures of HPC</B></U></A></div> <div> <A HREF="id61.htm" TARGET="_top" TITLE="Terms Conditions"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Terms & Conditions</B></U></A></div> <div> <A HREF="id62.htm" TARGET="_top" TITLE="Employment"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Employment</B></U></A></div> <div> <A HREF="id60.htm" TARGET="_top" TITLE="Handy Engineering Conversions Calculato"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Handy Engineering Conversions & Calculators</B></U></A></div> <div> <A HREF="id71.htm" TARGET="_top" TITLE="Links to our Favorite Sites"><U><B><IMG BORDER="0" SRC="Wing0a73007700c8ffffff00.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Links to our Favorite Sites</B></U></A></div> </td> <td valign="top" BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>     </B></div> <div> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="815" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 82 ><NOBR><div> <B>Phone:       440-684-0601</B></div> <div> <B>Fax:            440-684-0656</B></div> <div> <B>Toll Free:   800-468-5404</B></div> <div> <B>Email: </B><A HREF="mailto:sales@hughes-primeau.com" TARGET="_top" TITLE="mailto:sales@hughes-primeau.com"><U><B>sales@hughes-primeau.com</B></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <B><IMG SRC="89aad4a0.jpg" border=0 width="173" height="74" ALIGN="BOTTOM" HSPACE="0" VSPACE="0">                 <IMG SRC="89bbb4c0.jpg" border=0 width="187" height="76" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </B></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 178 WIDTH="252"><div> <B>Hughes-Primeau Controls celebrates the life and work of Henry G. Hughes</B></div> <div> <B>1933-2006</B></div> <div> <A HREF="id20_henry_g__hughes.htm" TARGET="_top" TITLE="Henry Hughes"><U><B><IMG SRC="75d83620.jpg" border=0 width="131" height="98" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </tD> <tD VALIGN=TOP WIDTH="544"><div> <B>Hughes-Primeau Controls combines 135+ years of selling engineered heat tracing systems with over 50 years of experience from Thermon.</B></div> <bR> <div> <B>No other company in Ohio, Western Pennsylvania, or West Virginia </B></div> <div> <B>can match our heat tracing solutions, inventory, nor expertise.</B></div> <div> <FONT SIZE="2" COLOR="#000000" FACE="Arial" ><IMG SRC="75c46490.jpg" border=0 width="70" height="73" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><B>      </B><FONT SIZE="2" COLOR="#000000" FACE="Arial" >    </FONT><B>         </B>A Drug Free Workplace</div> </tD> </tR> </TABLE></div> <bR> <bR> <DIV ALIGN="LEFT"></DIV> <div>  <A NAME="laws_of_affinity_calculation_guide"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Laws of Affinity Calculation Guide</div> <bR> <div> <B>The Affinity Laws:</B></div> <bR> <div> The turbo machine affinity laws are common used for pumps and fans to calculate capacity, head and power consumption when changing speed or wheels diameters.</div> <bR> <div> <B>The Affinity Laws</B> of a centrifugal pump or fan express the effect on capacity, head and power consumption of a pump or fan due to: </div> <div> different<B> speed</B> - revolutions per minute (rpm) </div> <div> geometrically similarity -<B> impeller diameter</B> </div> <bR> <div> <B>Changing the Pump or Fan Speed (rpm)</B></div> <div> Changing the speed (rpm, rev/min) of the pump or fan: </div> <div> Capacity</div> <div> <I>Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> </I>(1)</div> <div> Head</div> <div> <I>H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = (N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I>)</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT> (2)</div> <div> Power</div> <div> <I>P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = (N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I>)</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>3</I></FONT><I> </I>(3)</div> <bR> <div> where</div> <div> <I>Q</I> = capacity</div> <div> <I>H</I> = <FONT SIZE="3" COLOR="#0000FF" FACE="Arial" ><U>head</U></FONT> </div> <div> <I>P </I>= power </div> <div> <I>N</I> = speed </div> <bR> <div> If the speed increase with 10%</div> <div> <IMG BORDER="0" SRC="Symb075c00b700f0ff000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">the volume increase 10%<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <IMG BORDER="0" SRC="Symb075c00b700f0ff000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">the head increase 21%<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <IMG BORDER="0" SRC="Symb075c00b700f0ff000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">the power increase 33 %<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Note! This mean that if we want to increase the volume flow in an existing system with 10% we have to increase the power with 33%. In general the motor and the power supply must be changed. </div> <bR> <div> <B>Changing the Impeller Diameter</B></div> <div> Changing the impeller diameter: </div> <div> Capacity</div> <div> <I>Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT> (4)</div> <div> Head</div> <div> <I>H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = (D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I>)</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> </I>(5)</div> <div> Power</div> <div> <I>P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = (D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>/ D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I>)</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>3</I></FONT><I> </I>(6)</div> <div> where </div> <div> <I>D </I>= impeller diameter</div> <div> Example - <FONT SIZE="2" COLOR="#0000FF" FACE="Arial" ><U>Pump Affinity Laws</U></FONT> </div> <bR> <div> <B>Pump Speed Changed (Impeller Size Constant):</B></div> <div> The initial flow is 100 GPM, the initial head is 100 ft, the initial power is 5 bhp, the initial speed is 1750 rpm and the final speed 3500 rpm.</div> <div> The final flow capacity can be calculated by transforming (1):</div> <div> <I>Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2 </I></FONT><I>/ N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1</I></FONT><I> = </I>(100 GPM) (3500 rpm) / (1750 rpm) = <U>200</U> GPM</div> <bR> <div> The final head can be calculated by transforming (2):</div> <div> <I>H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>(N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> / N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1</I></FONT><I>)</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT> = (100 ft) ((3500 rpm) / (1750 rpm))<FONT SIZE="1" COLOR="#000000" FACE="Arial" >2</FONT> = <U>400</U> ft</div> <bR> <div> The final power consumption can be calculated by transforming (3):</div> <div> <I>P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1</I></FONT><I> (N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2 </I></FONT><I>/ N</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1</I></FONT><I>)</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>3</I></FONT><I> </I>= (5 bhp) ((3500 rpm) / (1750 rpm))<FONT SIZE="1" COLOR="#000000" FACE="Arial" >3</FONT> = <U>40</U> bph</div> <bR> <div> <B>Pump Impeller Diameter Changed (Pump Speed Constant)</B></div> <div> The impeller diameter is changed from 8" (inch) to 6" (inch).</div> <div> The final flow capacity can be calculated by transforming (4):</div> <div> <I>Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = Q</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2 </I></FONT><I>/ D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1</I></FONT> = ( 100 GPM) (6") / (8") = <U>75</U> GPM</div> <bR> <div> The final head can be calculated by transforming (5):</div> <div> <I>H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = H</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT>(<I>D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2 </I></FONT><I>/ D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1</I></FONT>)<FONT SIZE="1" COLOR="#000000" FACE="Arial" >2</FONT> = (100 ft) ((6") / ( 8"))<FONT SIZE="1" COLOR="#000000" FACE="Arial" >2</FONT> = <U>56,25</U> ft</div> <bR> <div> The final power consumption can be calculated by transforming (6):</div> <div> <I>P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2</I></FONT><I> = P</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1 </I></FONT><I>(D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>2 </I></FONT><I>/ D</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>1</I></FONT>)<FONT SIZE="1" COLOR="#000000" FACE="Arial" >3</FONT> = (5 bhp) ((6") / ( 8"))<FONT SIZE="1" COLOR="#000000" FACE="Arial" >3</FONT> = <U>2,1</U> bph</div> <bR> </td> </tr></table></body>