Chapter:

Properties-of-fluid

Oil of viscosity `mu=0.20`Ns/`m^2` fills small gap of thickness y=0.2 mm as shown in figure. Neglecting fluid stress exerted on circular underside, find torque required to rotate truncated cone at speed of 90 rpm. What is rate of heat generation, in joules per second, if value of `alpha=45^0` a=45 mm and b=60 mm.

SOLUTION:

Oil of viscosity `mu=0.20`Ns/`m^2` fills the small gap of thickness y=0.2 mm as shown in the figure. Neglecting the fluid stress exerted on the circular underside, find the torque required to rotate the truncated cone at speed of 90 rpm. What is the rate of heat generation, in joules per second, if the value of `alpha=45^0` a=45 mm and b=60 mm.

Given,

Vertex angle = `2 alpha`

Viscosity of the oil,`mu=0.2`Ns/`m^2`

Speed of rotation, `N= 90` rpm

a=45 mm

b=60 mm

Thickness of the oil layer, `t=0.2 mm=0.0002 m`

Let us consider an elementary area `dA` at a height h from the apex of a cone and let the radius at that height be  r as shown in figure. Let ds be the inclined length of el....Show More