Chapter 6, Problem 6.38P

Interpretation Introduction

Interpretation: The mass flow rate through the two different lines of the pipe is to be determined by using the energy balance equation.

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:-

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

The notations used in equation (1) are:-

P₁ and P₂ are pressure at inlet and outlet of the pipe

v₁ and v₂ are velocity at inlet and outlet of the pipe

Z₁ and Z₂ are the locations of the fluid

  $\text{ρ}$ = Density of the water

H = Head developed

h_L = Head loss in the pipe

g = Acceleration due to gravity

The mass flow rate is given as,

  $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}\text{=}\text{ρ}\text{×A×v}$ ...... (2)

  $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}$ = Mass flow rate through the pipe

A = Area of pipe

v = Velocity of water