Chapter 5, Problem 5.12P

Interpretation Introduction

Interpretation: The force of the fluid on the plate at stationary and moving position is to be determined.

Concept introduction: The flow in which the density of the fluid does not change with the time is called incompressible fluid and the volume in which the fluid is working is known as the control volume.

For steady incompressible flow, the force for a particular control volume is given as,

  ${\displaystyle \sum {\text{F}}_{\text{x}}}\text{=}{\displaystyle {\iint }_{\text{C}\text{.V}\text{.}}{\text{v}}_{\text{x}}\text{ρ(<mover accent="true"> <mo>v</mo> <mo>→</mo></mover>}\text{.<mover accent="true"> <mo>n</mo> <mo>→</mo></mover> )dA}}$   ……. (1)

The notations used here are,

F_x = Force in the x-direction

v_x = Velocity in the given direction

  $\text{ρ}$ = Density of the fluid

A = Area of the jet

The area of the jet is given as,

  $\text{A}\text{=}\frac{\text{Q}}{{\text{v}}_{\text{j}}}$   ……. (2)

The notations used here are,

Q = Flow rate of the fluid towards jet

v_j = Velocity of the jet