SAE-30 oil is used as a lubricant for crankshaft journal bearings in a car engine. The shaft has a diameter of d = 8 cm, a length of L = 3 cm, and it is rotating at a speed of ω = 3,600 rpm. The gap width between the shaft and bearing is h = 0.005 cm. Mechanic Jim wonders how lubricants with different viscosities will affect the performance of the engine.
Derive an expression for the torque required
to turn the shaft in terms of the viscosity of the lubricant. What is
the value of torque when SAE-30 oil is used as the lubricant?
Assume the rotating shaft and bearing are concentric, and no pressure
gradient exists in the direction of the flow.
Base the analysis on flow between parallel plates. The top
plate moves at a constant velocity while the bottom plate is fixed.
SAE-30 oil is a Newtonian fluid, and its viscosity is
9.6 (10-3) N-s/m2.
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