A solid cylindrical object with diameter d = 3 in and length L = 6 in. is pushed

Question

A solid cylindrical object with diameter d = 3 in and length L = 6 in. is pushed through a stationary cylindrical pipe by a force of F, as shown below. A thin layer of SAE30 oil coats in the inside of the pipe, such that the 50 mil gap between the surface of the solid and the pipe wall is filled with oil. You may assume the remainder of the pipe is filled with air at atmospheric pressure, on both sides of the solid object. A sketch is not required, but will be useful for setting up the problem. Using only USCS units, determine the value of F required to push the solid cylinder at a constant velocity of 6 in/s.

Explanation / Answer

Shear stress = (dv/dh) = v/h

Shear force F = shear stress*area = v/h *dL

= (1.15*10^-7)*(6*0.0254)/(50*0.0254*10^-3) *3.14*3*(0.0254)*(6*0.0254) = 5.03*10^-7 N

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