Metric conversion of formula

• posted

"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.

• posted

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.)

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