Where does this equation come from? 1

[drir]

Hi,

In a text book I found an equation for the volumetric flow rate of air through a channel (tube). I can't find from where the equation is coming, someone an idea?

The equation which I mean is: Q = - pi*d^4/(128*viscosity)* dp/dx

I know that Q = A*v = pi*d^2/4 *v

Also from the simplified equation of motion 'v' can be calculated as:

dp/dx = viscosity * ddv/ddy (dd = second derivative)

from this equation v = ?? if I fill v in, in Q = pi*d^2/4 *v will this give Q = - pi*d^4/(128*viscosity)* dp/dx ??

 

[25362]

It could be the formula is a derivation of the famous Hagen-Poiseuille law for friction dissipation in a horizontal pipe:

Q = [[π]r⁴/(8[μ])](-[Δ]p/L)​

Replacing r = D/2, one gets:

Q = [[π]D⁴/(128[μ])](-[Δ]p/L)​

 

[jmw]

For all things flowing in pipes and fittings, acquire a copy of the "Flow of fluids through valves fittings and pipe" Crane 410 or 410M.
Cheresources.com devotes a lot of attention to flow problems using this handbook.
This is a book you need to own if this is more than a passing interest in flow.


JMW

http://www.ViscoAnalyser.com

 

[drir]

Indeed it is the Hagen-Poiseuille equation! Thanks I couldn`t remember the name!!