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.

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Netta00 Netta00 · Answer 1 · 2019-11-05T11:12:21+01:00

Answer:

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

[tex]\rho_1=\dfrac{P_1}{RT_1}[/tex]

[tex]\rho_1=\dfrac{350}{0.287\times 450}[/tex]

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

[tex]h_1+\dfrac{C_1^2}{200}+Q=h_2+\dfrac{C_2^2}{2000}[/tex]

For ideal gas

Δh = CpΔT

by putting the values

[tex]1.011\times 450+\dfrac{3^2}{200}+Q=1.011\times 300+\dfrac{460^2}{2000}[/tex]

[tex]Q=1.011\times 300+\dfrac{460^2}{2000}-\dfrac{3^2}{200}-1.011\times 450[/tex]

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