Calculating volume flow rate per unit width of a plate ( Fluid Mechanics )


by iwearnexus
Tags: fluid dynamics, mechanical engineer, thermodynamics, volumetric flow rate
iwearnexus
iwearnexus is offline
#1
Nov19-12, 04:45 PM
P: 2
This is the question

The flow of a fluid between two large flat parallel plates normal to the y direction is fully developed and steady. The plates are a distance 2h apart in the y direction and the velocity profile, assuming y=0 is at the midpoint between the plate is V(y) = V_0(1-(y/h)^2) where V_0 is the centreline velocity. Derive equations for volume flow rate per unit width of the plate and the shear stress at the wall. Sketch and explain your shear stress result.


I know that d(...)/dx and d(...)/dt are zero since the flow is fully developed and steady.

also Volume flow = velocity x area.

how do i use this information to get the answer?

Im stuck.
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darkside00
darkside00 is offline
#2
Nov19-12, 07:27 PM
P: 83
you can try integrating with respect to y giving the area under the curve, right? while setting the limits properly. I'm sure you know shear stress = mu*(dV/dy)

also, this is homework


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