Fluid flow between parallel plates

[hamurabi]

Homework Statement

The velocity distribution for laminar flow between parallel plates is given by
u/umax = 1-(2y/h)2
where h is the distance separating the plates and the origin is placed midway between the plates.
Consider flow of water at 15 0C with maximum speed of umax=0.05 m/s and h=5 mm. Calculate the
force on a 0.3 m2 section of the lower plate and give its direction.

Homework Equations

Given in the problem and perhaps P = F/A

The Attempt at a Solution

Well I know that the maximum velocity will occur at the origin i.e y=0 and that the velocity at the plates is zero. So the maximal force would occur also at the origin - Would I have to get the y-component of the velocity?

I am guessing that the temperature is given so that we can get density (0.999) and viscosity (1.78 cp) from tables - or this may just be a red herring

Now the thing I am having problems with is linking the velocity with an equation to get pressure so that I can calculate the force.

Any guidance would be much appreciated!

 

[Chestermiller]

Homework Statement

The velocity distribution for laminar flow between parallel plates is given by
u/umax = 1-(2y/h)2
where h is the distance separating the plates and the origin is placed midway between the plates.
Consider flow of water at 15 0C with maximum speed of umax=0.05 m/s and h=5 mm. Calculate the
force on a 0.3 m2 section of the lower plate and give its direction.

Homework Equations

Given in the problem and perhaps P = F/A

The Attempt at a Solution

Well I know that the maximum velocity will occur at the origin i.e y=0 and that the velocity at the plates is zero. So the maximal force would occur
also at the origin - Would I have to get the y-component of the velocity?

The maximum velocity will occur at the plates, not at y = 0. The shear rate of the fluid is given by $$\frac{du}{dy}=-u_{max}\frac{4y}{h^2}$$At the lower plate, y =-h/2, the shear rate is $$\frac{du}{dy}=\frac{2u_{max}}{h}=20\ s^{-1}$$

I am guessing that the temperature is given so that we can get density (0.999) and viscosity (1.78 cp) from tables - or this may just be a red herring

If the viscosity is1.78 cp, this means that the shear stress at the lower plate is: $$\tau=\eta \frac{du}{dy}=0.0178 (20)=0.356\ dynes/cm^2=0.0356\ Pa$$

Now the thing I am having problems with is linking the velocity with an equation to get pressure so that I can calculate the force.

Any guidance would be much appreciated!

They are asking for the shear force, not the normal force.