Answer to Question #204808 in Mechanical Engineering for lobaya

Question

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

Answer 1

Given:

$\mu=1\ poise=0.1N\cdot s/m^2$

Diameter of shaft $D=10cm=0.1m$

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

Speed of shaft $N=150\ r.p.m.$

Tangential speed of shaft is given by

$$u=\dfrac{\pi DN}{60}=\dfrac{\pi\cdot0.1m\cdot150\ r.p.m.}{60}=\dfrac{\pi}{4}m/s$$

Change of velocity between shaft and bearing

$$du=u-0=\dfrac{\pi}{4}m/s$$

Mathematically

$$\tau=\mu\dfrac{du}{dy}=0.1N\cdot s/m^2\times\dfrac{\dfrac{\pi}{4}m/s}{1.5\cdot10^{-3}m}=$$ $$=\dfrac{50\pi}{3}N/m^2\approx52.360 N/m^2$$