Answer to Question #226484 in Mechanics | Relativity for Aboody

Question

1.    A lubricated shaft of 200mm radius rotates inside a concentric sleeve bearing of 205mm radius. Determine the viscosity of the fluid, which fills the space between the sleeve and the shaft if a torque of 1.5N.m is required to maintain an angular velocity of 120rpm.take length of sleeve as 450mm.

Answer 1

Gives

∆r=205mm-200mm=5mm

Torque=1.5Nm

Hight(h)=450mm

$w=2\pi\times\frac{120}{160}=4\pi rad/sec$

Linear velocity

$v=rw$

$\frac{dv}{dr}=\frac{v}{r}=\frac{rw}{r}=w$ =4$\pi$

$\tau=rF$

$F=\frac{\tau}{r}$

$F=\frac{1.5}{205\times10^{-3}}=7.31N$

Area=$2\pi rh$

Put value

$A=2\pi \times205\times10^{-3}450\times10^{-3}=0.58m^2$

Newton's law

Force

$F=-\eta A\frac{dv}{dr}$

$\eta=\frac{F}{A\frac{dv}{dr}}$

$\eta=\frac{7.31}{{0.58}\times4\times3.14}=1.0034$ $Nsec/m^2$