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.

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

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

For ideal gas

Δh = CpΔT

by putting the values

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

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