5. Air with a mass flow rate of 2.3 kg/s enters a horizontal nozzle operating at

Question

5. Air with a mass flow rate of 2.3 kg/s enters a horizontal nozzle operating at steady state at 450K, 350kPa, and velocity of 3m/s. At the exit, the temperature is 300K and the velocity is 460m/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 and its surroundings, in kW. Specify whether the heat transfer is to or from the air.

Some other information also provided which may or may not apply to this problem g=9.8 m/s^2, density of water 1000 kg/m^3, specific heat of liquid water 4.18 kJ/(kg*C), specific heats of air c_v=0.718 kJ/(kg*C) and c_p=1.0 kJ/(kg*C).

Explanation / Answer

5. given

mass flow rate, R = 2.3 kg/s

Ti = 450 K

Pi = 350 kPa

Vi = 3 m/s

Te = 300 K

Ve = 460 m/s

Cp = 1.011 kJ/kg K

a. mass flow rate in a nozzle is constant, from consevation of mass

hence

R = rhoi*Ai*Vi = rhoe*Ae*Ve

now, at exit

from ideal gas equation

Pe = rhoe*R'Te

R' = 286.9 J/kg K

hence

rhoi = Pi/R'*Ti = 2.71097168 kg /m^3

Ai = R/rhoi*Vi = 0.2828014 m^2

b. heat released to the atmosphere = R*Cp*(Ti - Te)

Q' = R*1011(450 - 300) = 348795 W

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