Question

Air enters a nozzle steadily at 2.21 kg/m3 and 40 m/s and leaves at 0.752 kg/m3 and 180 m/s. If the inlet area of the nozzle is 90 cm2, determine (a) the mass flow rate through the nozzle, and (b) the exit area of the nozzle.
(a) 0.796 kg/s,
(b) 58 cm2

Answer 1

Answer

Given,

Air enter density, ρ₁ = 2.21 kg/m³

speed of entry, v₁ = 40 m/s

Air exit density , ρ₂ = 0.752 kg/m³

speed of exit, v₂ = 180 m/s

Inlet area = 90 cm²

a) mass flow rate through nozzle.

   $m = \rho_1 A_1 v_1$

   $m = 2.21\times 90\times 10^{-4}\times 40$

            m = 0.796 kg/s

b) exit area

  Using continuity equation

  $\rho_1 A_1 v_1=\rho_2A_2 v_2$

  $A_2 = \dfrac{\rho_1 A_1 v_1}{\rho_2 v_2}$

  $A_2 = \dfrac{2.21\times 90\times 40}{0.752\times 180}$

  $A_2 = 58\ cm^2$

Exit area of nozzle is equal to $58\ cm^2$