Chapter 6, Problem 6.15P

Interpretation Introduction

Interpretation: The pressure inside the pump at the inlet point is to be calculated by applying the energy balance equation.

Concept introduction: The energy balance across the pump is given by the Bernoulli’s equation in which the sum of Potential energy, Kinetic energy and Pressure energy is constant. The Bernoulli equation across 2 points of any system is given by:

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

P₁and P₂are pressure at 2 points of the pipe.

v₁ and v₂ are velocity at 2 points of the pipe.

Z₁ and Z₂ are the locations at 2 points.

  $\begin{array}{l}\text{ρ}\text{=}\text{Density}\text{of water}\text{=}\text{62}{\text{.4lbs/ft}}^{\text{3}}\\ \text{g}\text{=}\text{Acceleration}\text{due}\text{to}\text{gravity}\end{array}$

The volumetric flow rate in air duct is given as

  $\text{Q}\text{=}\text{A×v}$   ............ (2)

Q = Volumetric flow rate of water

A = Area of pipe

v = Velocity at 2 points of pipe