Chapter 6, Problem 6.21P

Interpretation Introduction

Interpretation: The airflow rate for the cushion and the power given to the compressor 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:-

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

The notations used in equation (1) are:-

P₁and P₂are pressure at inlet and outlet of the cushion

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

Z₁ and Z₂ are the locations of the fluid

  $\text{ρ}$ = Density of the air

g = Acceleration due to gravity

The power delivered is given as,

  $\text{<msup> <mo>P</mo> <mo>′</mo></msup>}\text{=}\text{ρgHQ}$  ..... (2)

Q = Flow rate of the air

  $\text{<msup> <mo>P</mo> <mo>′</mo></msup>}$ = Power given to the air by the compressor

H = Head developed

The volumetric flow rate is given as,

  $\text{Q}\text{=}\text{L}\text{×}\text{C}\text{×}\text{v}$  ..... (3)

L = Perimeter of the skirt

v = Velocity of air

C = Ground clearance