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

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The discussion focuses on calculating the volume flow rate per unit width of fluid flow between two parallel plates, with a given velocity profile. The flow is steady and fully developed, allowing for simplifications such as zero derivatives with respect to x and t. To find the volume flow rate, the velocity must be integrated over the area between the plates, using the provided limits. Shear stress at the wall can be determined using the equation shear stress = mu*(dV/dy), where mu is the dynamic viscosity. The participants emphasize the need for proper integration and understanding of the shear stress concept in fluid mechanics.
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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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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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