Chapter 4, Problem 4.4P

Interpretation Introduction

Interpretation: The initial height of the water in the reservoir is to be determined for the given power of the pump.

Concept introduction: Whenever there is a case of delivering some amount of fluid from one place to another by suction line to discharge line in a pump, Bernoulli’s equation for energy balance is to be applied which states that the sum of potential energy, kinetic energy and pressure energy is constant. The equation for the same is,

  $\frac{{\text{P}}_{\text{1}}}{\text{ρ}}\text{+}{\text{gZ}}_{\text{1}}\text{+}\frac{{\text{v}}_{\text{1}}{}^{\text{2}}}{\text{2}}\text{+}\text{ηW}\text{=}\frac{{\text{P}}_{\text{2}}}{\text{ρ}}\text{+}{\text{gZ}}_{\text{2}}\text{+}\frac{{\text{v}}_{\text{2}}{}^{\text{2}}}{\text{2}}\text{+}{\text{h}}_{\text{f}}$ .... (1)

In the above formula, the notations used are,

P₁ and P₂ are the pressures at suction and discharge line respectively.

v₁and v₂ are the velocities at inlet and outlet of the pump respectively.

g is the acceleration due to gravity

Z₁ and Z₂ are the initial and final height of the water in the pump.

h_f = Frictional losses in the pump

W = Amount of work done

  $\text{η}$ = Pump efficiency

  $\text{ρ}$ = Liquid density

The power delivered by the pump is given as,

  $\text{P}\text{=}\text{ηWρQ}$ .... (2)

Here, P is the power delivered by the pump

Q is the flow rate of the pump