Question

Air with a mass flow rate of 2.3 kg/s enters a horizontal nozzle operating at steady state at 450 K, 350 kPa, and velocity of 3 m/s. At the exit, the temperature is 300 K and the velocity is 460 m/s. Using the ideal gas model for air with constant c_p = 1.011 kJ/kg*K, determine

(a) the area at the inlet, in m^2

(b) the heat transfer between the nozzle at its surroundings in kW.

(c) Specify whether the heat transfer is to or from the air.

Answer 1

Given that

Mass flow rate ,m=2.3 kg/s

T₁=450 K

P₁=350 KPa

C₁=3 m/s

T₂=300 K

C₂=460 m/s

Cp=1.011 KJ/kg.k

For ideal gas

P V = m R T

P = ρ RT

`\rho_1=(P_1)/(RT_1)`

`\rho_1=(350)/(0.287* 450)`

ρ₁=2.71 kg/m³

mass flow rate

m= ρ₁A₁C₁

2.3 = 2.71 x A₁ x 3

A₁=0.28 m²

Now from first law for open system

`h_1+(C_1^2)/(200)+Q=h_2+(C_2^2)/(2000)`

For ideal gas

Δh = CpΔT

by putting the values

`1.011* 450+(3^2)/(200)+Q=1.011* 300+(460^2)/(2000)`

`Q=1.011* 300+(460^2)/(2000)-(3^2)/(200)-1.011* 450`

Q= - 45.49 KJ/kg

Q =- m x 45.49 KW

Q= - 104.67 KW

Negative sign indicates that heat transfer from air to surrounding