Chapter 5, Problem 5.27P

Interpretation Introduction

Interpretation:

The amount of torque being exerted on the given impeller by the fluid is to be calculated along with the required amount of power to drive the pump.

Concept Introduction:

Torque is defined as the turning effect due to the rotational force being applied on an object. It is also known as moment or moment of forces.

The general equation written for the total moment of all forces acting on a controlled volume is:

  ${\displaystyle \sum M}={\displaystyle {\iint }_{C.S}\left(r\times v\right)\rho \left(v\cdot n\right)dA}+\frac{\partial }{\partial t}{\displaystyle {\iiint }_{C.V}\left(r\times v\right)\rho dV}$......... (1)

Here, C.S is the control surface over which the integral dA is taken, C.V is the control volume over which the integral dV is taken, $\rho$ is the density of the fluid, $v$ is the velocity vector, $n$ is the direction of the vector $v$ , $r$ is the position vector, $v\cdot n$ is a dot product and $\left(r\times v\right)$ is a cross product.

Power required per unit time is defined in terms of moment of force ( M ) and angular speed $\left(\omega \right)$ is:

  $P=M\cdot \omega$......... (2)