Chapter 7, Problem 7.22P

Interpretation Introduction

Interpretation:

The viscosity of the fluid contained between the gap of the two cylinders is to be calculated.

Concept Introduction:

Newton’s law of viscosity is defined as:

  ${\tau }_{yx}=\mu \frac{d{v}_x}{dy}$ .... (1)

Here, ${\tau }_{yx}$ is shear stress in y-x direction, $\mu$ is the viscosity of the fluid, and $\frac{d{v}_x}{dy}$ is the shear strain.

Velocity of a cylinder is further defined in terms of its angular velocity $\left(\omega \right)$ and radius $\left(R\right)$ as:

  $v=\omega R$ .... (2)

In terms of number of rotations $\left(N\right)$ , angular velocity is defined as:

  $\omega \left(\text{rad}/\text{s}\right)=\frac{2\pi N\left(\text{rpm}\right)}{60}$ .... (3)

The relationship between the average shear stress $\left(\tau \right)$ , the force applied on the fluid $\left(F\right)$ , and the cross sectional area $\left(A\right)$ to which the perpendicular force is applied is:

  $F=\tau A$ .... (4)

Torque $\left(T\right)$ applied by the rotating shaft on which force F is applied with radius Ris defined as:

  $T=FR$ .... (5)