A 10.00-cm shaft rides in an 10.03-cm sleeve 12 cm long, the clearance space (assumed to be uniform) being filled with lubricating oil at 40ºC (µ = 0.11 Pa.s). Calculate the rate at which heat is generated when the shaft turns at 100 rpm.
Text Solution
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CHECK THE SOLUTION.
Sol. dv = ꞷ(circumference) = 100/60[ π (0.10)] = 0.5236 m/s
dx = (0.1003 – 0.1000)/2 = 0.00015 m
τ = µ(dv/dx) = (0.11) (0.5236)/0.00015) = 384.0 N/m 2 F f = τ A = 384.0 [ π (0.12) (0.10)] = 14.48 N
Rate of energy loss = F f v = (14.48) (0.5236) = 7.852 N.m/s = 7.582 W
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