Find the force exerted by the oil on the shaft

[karius]

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? :(

Thanks in advance

 

[Studiot]

Hello Karius, welcome to Physics Forums.

Revision or not the rules here reuqire you to show us some attempted working before help is offered.

So what have you calculated so far?

 

[karius]

Well to be honest, I'm not sure whether this is correct or not, but this is what I have so far.
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 =/

 

[Studiot]

velocity gradient = v/t

v = peripheral velocity, t = film thickness

viscous shear force = $\eta$ x velocity gradient

viscous force on shaft = shear stress x surface area

power absobed by friction = viscous force x peripheral velocity

Is this enough help?