Chapter 6, Problem 6.24P

Interpretation Introduction

Interpretation: The gage pressure on the auto is to be determined by using the energy balance equation.

Concept introduction: The Energy balance across the two stations 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 two pints

v₁ and v₂ are velocity at two points

Z₁ and Z₂ are the locations of the fluid

  $\text{ρ}$ = Density of the air

h_L = Head loss in the section

H = Head developed

g = Acceleration due to gravity

The gage pressure is the difference between the pressure at a particular point and the atmospheric pressure.

  ${\text{P}}_{\text{g}}\text{=}\text{P}\text{-}{\text{P}}_{\text{atm}}$   ...... (2)

P = Pressure at a point

P_atm = Atmospheric pressure

P_g = Gage pressure