Fluid Mechanics Problem: Calculate Force on Lower Plate

[JSBeckton]

I'm struggling with a fluid mechanics problem:

The velocity distribution for laminar flow is given by
U/Umax = 1 -[2y/h]^2
h = dist between plates. origin is midway between plates, Consider the flow of water at 15 degrees C with max speed .005 m/s and h=1mm. Calculate the force on a 1m^2 section of the lower plate and give its direction.

Viscosity at 15 degrees C = 1.114x10^-3
What direction should I be going in here? Do I need to use the velocity equation to solve for U and then find the force with a different equation?
Thanks for any help.

 

[jaap de vries]

Assuming the flow is fully developed which it seems to be judging by the 1-D equation you gave the shear stress at the wall is simply

tau = mu du/dy, (evaluated a y = -0.5*h)

where mu is the viscosity.

du/dy = Umax*(8y/h^2), which becomes -8/2h= Umax*(-4/h) = 0.005*(-4/0.001) = -20

times the viscosity this becomes,

1.114*10^-3*-20 = -22.28 N/m^2

Since the area is 1 m^2 the net force of the plate on the fluid is 22.28 [N] in the negative x-direction

I hope this was of any help. I am pretty sure you have to use the velocity gradient at the bottom location. I am tired so I may have made a mistake but the principle should be pretty clear

Jaap

 

[JSBeckton]

Thanks, it helped.