Question

A viscometer may be created by using a pair of closely fitting concentric cylinders and filling the gap between the cylinder with the fluid whose viscosity will be measured. Assuming that the velocity profile in the gap is linear, calculate coefficient of viscosity if inner diameter is 75mm, outer diameter is 75.04mm, Torque is 0.021 N/m and w is 100 rpm.

Answer 1

The viscosity of the fluid is 6.05 Pa-s

Step-by-step explanation:

The viscosity obtained from a rotating type viscometer is given by the equation

`\mu =(3Tt)/(2\pi \omega R_o(R_o^3-R_i^3))`

where

T is the torque applied in the viscometer

't' is the thickness of gap

`\omega` is the angular speed of rotation

`R_o,R_i` are the outer and the inner raddi respectively

Since it is given that

`\omega =100rpm=(100* 2\pi )/(60)=10.47rad/sec`

Applying the values in the above relation we get

`\mu =(3* 0.021* 0.02* 10^(-3))/(2\pi * 10.47* 37.5* 10^(-3)(37.52^3-37.5^3)* 10^(-9))=6.04Pa-s`