Chapter 6, Problem 6.32P

Interpretation Introduction

Interpretation:

The flow rate or the rate of discharge of the pump with frictional head loss is to be calculated.

Concept introduction:

The Energy balance across the pipe is given by the Bernoulli’s equation in which the sum of Potential head, Kinetic head and Pressure head is constant. The Bernoulli equation across 2 points of any system is given by: -

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

P₁ and P₂ are pressure at 2 points of the pipe

v₁ and v₂ are velocity at 2 points of the pipe

Z₁ and Z₂ are the locations of the liquid.

  $\begin{array}{l}\text{ρ}\text{=}\text{Density}\text{of}\text{liquid}\\ \text{g}\text{=}\text{Acceleration}\text{due}\text{to}\text{gravity}\end{array}$

h_f = Friction head loss

The flow rate is given as,

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

Q = Flow rate of liquid

A = Area of pipe

v = Velocity of liquid