Chapter 6, Problem 6.6P

Interpretation Introduction

Interpretation: The stagnation temperature of the air at the given temperature and pressure is to be determined.

Concept introduction: The temperature at which a fluid is brought to rest adiabatically without any shaft work generation is called the stagnation temperature.

The stagnation temperature is given as,

  ${\text{T}}_{\text{s}}\text{=}\text{T}\text{+}\frac{{\text{u}}^{\text{2}}}{{\text{2c}}_{\text{p}}}$ ....... (1)

The notations used here are,

T_s = Stagnation temperature

T = Air temperature

u = Speed of air

c_p = Specific heat capacity

The speed of air is given as,

  $\text{u}\text{=}\text{Ma}\sqrt{\frac{\text{γp}}{\text{ρ}}}$ ....... (2)

The notations used here are,

Ma = Mach number = $\frac{\text{Speed}\text{of}\text{air}}{\text{Speed}\text{of}\text{sonic}}$

  $\text{γ}$ = Heat capacity ratio

p = Pressure of the air

  $\text{ρ}$ = Density of the air

The density of a air is given as,

The density of air can be given as,

  $\text{ρ}\text{=}\frac{\text{PM}}{\text{RT}}\mathrm{.......}(3)$

In the equation (3), notations used are,

P is the pressure at which air enters

M is the molecular weight of air

R is the Universal Gas constant

T is the temperature at which air enters