Answer to Question #204808 in Mechanical Engineering for lobaya

Question #204808

3. Determine the intensity of shear of an oil having viscosity =1 poise. The oil is used for lubricating the clearance between a shaft of diameter 10cm and its journal bearing. The clearance is 1.5 mm and the shaft rotates at 150 r.p.m


1
Expert's answer
2021-06-09T16:37:01-0400

Given:

μ=1 poise=0.1Ns/m2\mu=1\ poise=0.1N\cdot s/m^2

Diameter of shaft D=10cm=0.1mD=10cm=0.1m

Distance between shaft and journal bearing dy=1.5mm=1.5103mdy=1.5mm=1.5\cdot10^{-3}m

Speed of shaft N=150 r.p.m.N=150\ r.p.m.


Tangential speed of shaft is given by



u=πDN60=π0.1m150 r.p.m.60=π4m/su=\dfrac{\pi DN}{60}=\dfrac{\pi\cdot0.1m\cdot150\ r.p.m.}{60}=\dfrac{\pi}{4}m/s

Change of velocity between shaft and bearing



du=u0=π4m/sdu=u-0=\dfrac{\pi}{4}m/s

Mathematically



τ=μdudy=0.1Ns/m2×π4m/s1.5103m=\tau=\mu\dfrac{du}{dy}=0.1N\cdot s/m^2\times\dfrac{\dfrac{\pi}{4}m/s}{1.5\cdot10^{-3}m}==50π3N/m252.360N/m2=\dfrac{50\pi}{3}N/m^2\approx52.360 N/m^2

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