Chapter 6, Problem 6.13P

Interpretation Introduction

Interpretation: The pressure at a particular point on the auto 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 liquid.

  $\text{ρ}$ = Density of the water

h_L = Head loss in the section

H = Head developed

g = Acceleration due to gravity

The density of air can be calculated as,

  $\text{ρ}\text{=}\frac{\text{PM}}{\text{RT}}\mathrm{.......}(2)$

In the equation (2), notations used are,

P is the pressure at which air

M is the molecular weight of air

R is the Universal Gas constant

T is the temperature of air

The pressure at the inlet for mercury is,

  ${\text{P}}_{\text{1}}\text{=}{\text{ρ}}_{\text{m}}\text{gh}$ ……. (3)

h = Initial reading of manometer

  ${\text{ρ}}_{\text{m}}$ = Density of mercury