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Old Sep 3rd 2011, 10:57 PM   #1
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Simple Viscosity Problem

A 10-kg block slides down a smooth inclined surface. Determine the terminal velocity of the block if the 0.1-mm gap between the block and the surface contains SAE 30 oil at 60 F. Assume the velocity distribution in the gap is linear, and the area of the block in contact with the oil is 0.1 m^2.

(the diagram shows a slope downward 20 degrees from the horizontal)
----
What I did:
T = 60 F = 15.56 C
Looked up viscosity of SAE 30 oil at 15.56 C:
mu = 0.8 N*s/m^2
h (height) = 0.1 mm = 1 * 10^-4 m

tau = F/A = mu * dv/dy
F = sin theta * mg

Rearranging with assumption that dv/dy is constant (linear velocity gradient mentioned in problem):

velocity = (tau * h)/mu = (sin (theta) * mgh)/(A * mu)
= (sin (20*pi/180)*10*9.8*10^-4)/(0.1*0.8) = 0.0419 m/s

The official textbook answer is 0.0883 m/s.

How do I get the correct answer?

EDIT: Converted this post from LaTeX to text.

Last edited by pramoda; Sep 4th 2011 at 09:09 AM. Reason: Converted this post from LaTeX to text.
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Old Sep 3rd 2011, 10:57 PM   #2
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I'm seeing: [LaTeX Error: Can't write to directory]

Is this board broken? Can I post basic LaTeX?
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Old Sep 4th 2011, 03:01 AM   #3
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I don't know about how to solve your problem, but for the LaTeX part, no, there is no LaTeX here. You might however generate a picture from here then copy/paste the link to the picture which appears. The only problem is that we are restricted to 6 images per post. You might hence want to put several equations in the same image.
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