Question

1. A piston having a diameter of 5.48 inches and a length of 9.50 in slides downward with a velocity, V, through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is 0.002 inches and the cylinder weighs 0.5 lb. Compute the velocity, V if the oil viscosity is 0.016 lb*s/ft
2. Assume the velocity distribution in the gap is linear. (answer: 0.0046 ft/sec) I need to understand this for my quiz so please work steps clearly. Will Rate!!!"

Answer 1

Answer:

V = 0.00459 ft/s  

Explanation:

Since the Piston is moving downwards with a constant velocity V, from the first Newton’s law we know that all vertical forces, must have zero resultant (their sum over vertical axis must equal to zero). Therefore, force that pulls the piston down, is equalized by force of viscous friction Fd= Fvf = 0.5lb (lb here is the pound-force unit). We will relate F ѵ f  with τ and from that derive the equation for V.

Fѵf = τ  . A

Where τ  = µ. du/dy = µ . V/b  , and A = π . D . l from this Follows:

Fѵf= (V.  A .µ )/b     V= ( Fѵf .b )/(A.µ)    

Placing all the known values in the equation ( remember  to transform inches to feet, by multiplying inches values with the factor 1/12), we obtain :  

ft2

V = ((0.5lb)   .   (0.002/12 ft))/(π   .   (5.48/12 ft)  .  (9.50/12 ft)  .  (0.016 lb.s/(ft^2 )))

V = 0.00459 ft/s  

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