Chapter 5, Problem 5.29P

Interpretation Introduction

Interpretation:

The amount of torque required to keep the given sprinkler stationary is to be determined.

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.