# Metric conversion of formula

"The Standard Handbook of Engineering Calculations "
gives the Poiseuille formula for head loss in pipes with laminar flow.
If I correctly interpret the figures given in brackets as the metric formula
Pd = 10^-4 x l x u x G / d^4
Pd is pressure drop (kPa ) l is pipe length, ( ? ) U is absolute viscosity ( Pa s ) G is flow rate ( l / s ) d is pipe diameter ( cm )
Is this correct, and should the pipe length be in meters ?
What is the conversion factor from cP ( centipoise ) to Pa s ( Pascal seconds ) ? I think 1000 cP = 1 Pa s but I'm not sure.
to further confuse me :-) the "Handbook of Chemistry and Physics " ( aka, the rubber handbook ) gives Poiseuille as
V = ( (Pi) x p x r^4 ) / ( 8 x l x ( Eta) )
V = volume flow ( cm^3 / s ) l = pipe length ( cm ) r = pipe radius ( cm ) p = pressure loss ( dynes / cm^2 ) ( Eta ) = viscosity ( Poise = dyne s / cm^2 )
What I really want is the formula in SI units.
I'm prity certain I have got a factor that's a fraction of (Pi)^4 missing from the first equation.
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Jonathan Barnes wrote:

You are correct. To convert from centipoise to Pa*s you multiply by 0.001 ("Fundamentals of fluid mechanics," Schetz and Fuhs, eds., Wiley, 1999, p. 213.)

My books have:
dP = 8 * mu * Q * L / ( pi*R^4 )
(This seems to agree with the second equation you gave, the one from the CRC handbook.)
where dP is pressure drop mu is viscosity Q is volume flow rate L is length pi is 3.15159... R is pipe radius
This formula should work in any consistent set of units, such as SI where dP is in Pa, mu is in Pa*s, Q is in cubic meters per second, L and R are in meters. (the CRC book seems to use cgs units.)
--------------050502070504030604040804 Content-Type: text/html; charset=us-ascii Content-Transfer-Encoding: 7bit
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> </head> <body bgcolor="#ffffff" text="#000000"> Jonathan Barnes wrote:<br>
<pre wrap=""> What is the conversion factor from cP ( centipoise ) to Pa s ( Pascal seconds ) ? I think 1000 cP = 1 Pa s but I'm not sure.
</pre> </blockquote> <br> &nbsp;&nbsp;&nbsp; You are correct. To convert from centipoise to Pa*s you<br> &nbsp;&nbsp;&nbsp;&nbsp; multiply by 0.001 ("Fundamentals of fluid mechanics," Schetz and Fuhs, eds.,<br> &nbsp;&nbsp;&nbsp;&nbsp; Wiley, 1999,&nbsp; p. 213.)<br> <br>
<pre wrap="">to further confuse me :-) the "Handbook of Chemistry and Physics " ( aka, the rubber handbook ) gives Poiseuille as
V = ( (Pi) x p x r^4 ) / ( 8 x l x ( Eta) )
V = volume flow ( cm^3 / s ) l = pipe length ( cm ) r = pipe radius ( cm ) p = pressure loss ( dynes / cm^2 ) ( Eta ) = viscosity ( Poise = dyne s / cm^2 )
What I really want is the formula in SI units.
I'm prity certain I have got a factor that's a fraction of (Pi)^4 missing from the first equation.
</pre> </blockquote> <br> &nbsp;&nbsp; My books have:<br> <br> &nbsp;&nbsp; dP = 8 * mu * Q * L / ( pi*R<sup>4</sup>)<br> <br> &nbsp;&nbsp; (This seems to agree with the second equation you gave, the<br> &nbsp;&nbsp; one from the CRC handbook.)<br> <br> &nbsp;&nbsp; where dP is pressure drop<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; mu is viscosity<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Q is volume flow rate<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; L is length<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; pi is 3.15159...<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R is pipe radius<br> <br> &nbsp;&nbsp; This formula should work in any consistent set of units, such as<br> &nbsp;&nbsp; SI where dP is in Pa, mu is in Pa*s, Q is in cubic meters per second,<br> &nbsp;&nbsp; L and R are in meters. (the CRC book seems to use cgs units.)<br> <br> &nbsp;<br> </body> </html>
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