Chapter 5, Problem 5.9P

Interpretation Introduction

Interpretation: The hourly energy cost for pumping the water is to be determined.

Concept introduction: The energy cost can be found by calculating the power required by the pump for the given amount of efficiency.

The power for FPS system is given as,

  $\text{P}\text{=}\text{ρHQ}$ .......... (1)

The notations used here are,

P = Power developed by the pump

  $\text{ρ}$ = Density of the fluid

g = Acceleration due to gravity

H = Head developed by the pump

Q = Flow rate by the pump

The Reynolds number is given as,

  $\text{Re = }\frac{\text{ρ<mover accent="true"><mo> v </mo><mo>¯</mo></mover> D}}{\text{μ}}$ .......... (2)

The notations used here are,

  $\text{<mover accent="true"><mo> v </mo><mo>¯</mo></mover>}$ = Average velocity of the fluid

D = Diameter of pipe

  $\text{μ}$ = Viscosity of the fluid

  $\text{ρ}$ = Density of fluid

The head developed by the pump is the sum of the original elevation of the pump and the head developed due to energy consumption by the pump.

The developed head in FPS units is calculated as,

  ${\text{h}}_{\text{f}}\text{=}\frac{{\text{2fL<mover accent="true"><mo> v </mo><mo>¯</mo></mover>}}^{\text{2}}}{\text{gD}}$ .......... (3)

L = Length of the pipe

The roughness parameter is given as, $\frac{\text{k}}{\text{D}}$ where k is roughness of the pipe. It shows how much friction is present in the pipe and with the help of the roughness parameter, f can be calculated from the friction factor chart.