Fluid Mechanics Viscosity Question

[karius]

Homework Statement

Hi guys,

I'm pretty new here, and long story short, I'm struggling a bit on a fluid mechanics question I've been doing for some revision.

A shaft 70 mm in diameter is being pushed at a speed of 400 mm/s through a bearing sleeve
70.2 mm in diameter and 250 mm long. The clearance, assumed uniform, is filled with oil
with kinematic viscosity ν = 0.005 m^2/s and density ρ = 900 kg/m^3. Find the force exerted by the oil on the shaft. (ans.: 990 N)

As you see, I have the answer given to me, but I do not quite get the working out. Can somebody please help me out? :(

Homework Equations

τ = µ*du/dy
τ = F/A = Shear Stress
du/dy: is the velocity change divided by the distance over which the change
occurs, i.e., velocity gradient
u: is the fluid velocity parallel to the applied force
μ: is the dynamic viscosity coefficient or more simply the viscosity of the fluid
y: is the transverse distance normal to the shear force.

The Attempt at a Solution

I have found µ (the dynamic viscosity coefficient) to come up to be 4.5kg/(ms).

Then I went on to find τ (Shear Stress) to be 7.2

And this is basically where I get stuck. Once again, I have no idea if I am on the correct path as this is my first time doing this kind of question =/

 

[Chestermiller]

Homework Statement

Hi guys,

I'm pretty new here, and long story short, I'm struggling a bit on a fluid mechanics question I've been doing for some revision.

A shaft 70 mm in diameter is being pushed at a speed of 400 mm/s through a bearing sleeve
70.2 mm in diameter and 250 mm long. The clearance, assumed uniform, is filled with oil
with kinematic viscosity ν = 0.005 m^2/s and density ρ = 900 kg/m^3. Find the force exerted by the oil on the shaft. (ans.: 990 N)

As you see, I have the answer given to me, but I do not quite get the working out. Can somebody please help me out? :(

Homework Equations

τ = µ*du/dy
τ = F/A = Shear Stress
du/dy: is the velocity change divided by the distance over which the change
occurs, i.e., velocity gradient
u: is the fluid velocity parallel to the applied force
μ: is the dynamic viscosity coefficient or more simply the viscosity of the fluid
y: is the transverse distance normal to the shear force.

The Attempt at a Solution

I have found µ (the dynamic viscosity coefficient) to come up to be 4.5kg/(ms).

Then I went on to find τ (Shear Stress) to be 7.2

And this is basically where I get stuck. Once again, I have no idea if I am on the correct path as this is my first time doing this kind of question =/

What did you get for the shear rate? I got 4000/sec. The shear stress is equal to the viscosity times the shear rate. That would give me a shear stress of 18000 Pa. What is surface the area over which this shear stress is acting?