Where does this equation come from?

[hermano]

Hi,

In a textbook 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 ??

 

[lightgrav]

Work is being done by the Pressure gradient, to friction with the walls, due to the viscosity. ... your Q is mass density times v dot dA, integrated over the tube's cross-section Area. the velocity goes to zero at the tube surface, and is maximum in its center.

 

[stonecoldgen]

the density comes from massXvolume

and the mass comes from 1/2mv^2=Ek
i hope this helped a little bit