Chapter 8, Problem 8.3P

Interpretation Introduction

Interpretation: The power required to drive the pump in previous linked question is to be determined.

Concept introduction:The power required for the mechanical work to be done is calculated by the Bernoulli’s Energy balance equation. Bernoulli’s equation states that the sum of Kinetic energy head, potential energy head and the pressure energy head is constant. The equation in its proper form is given as,

  $\frac{{\text{P}}_{\text{1}}}{\text{ρg}}\text{+}{\text{Z}}_{\text{1}}\text{+}\frac{{\text{v}}_{\text{1}}{}^{\text{2}}}{\text{2g}}\text{+}\text{ηH}\text{=}\frac{{\text{P}}_{\text{2}}}{\text{ρg}}\text{+}{\text{Z}}_{\text{2}}\text{+}\frac{{\text{v}}_{\text{2}}{}^{\text{2}}}{\text{2g}}\text{+}{\text{h}}_{\text{f}}\mathrm{.......}\text{(1)}$

In the above formula, the notations used are,

P₁ is the absolute pressure at the reboiler unit.

P₂ is the pressure at the delivering end.

Z₁ is the initial elevation unit

Z₂ is the elevation at the delivering end

v₁ is the initial velocity of the pump

v₂ is the velocity at the discharge line of the pump

g is the acceleration due to gravity

H is the total head developed

  ${\text{h}}_{\text{f}}$ is the frictional head

  $\text{ρ}$ is the density of the fluid

  $\text{η}$ is the efficiency of the pump

The power of the pump is given as,

  

   is the mass flow rate of the fluid

P is the power of the pump