Problems On Nozzles
Problems 1-5 are from ‘Applied Thermodynamics - For Engineering Technologists’ by Eastop TD &
McConkey, page 325.
Problem 1
Calculate the throat and exit areas of a nozzle to expand air at a rate of 4.5 kg/s from 8.3 bar, 327 0C into a space at 1.38 bar. Neglect the inlet velocity and assume isentropic flow.
3290 mm2; 4840 mm2
Problem 2
It is required to produce a stream of helium at the rate of 0.1 kg/s travelling at sonic velocity at a temperature of 150C. Assume isentropic flow, negligible inlet velocity and a back pressure (= exit pressure) of 1.013 bar, calculate:
(i) the required inlet pressure and temperature;
(ii) The exit area of the nozzle.
Molar mass of helium is 4 kg/kmol, and = 1.66
2.077 bar; 1100C; 593 mm2
Problem 3
Recalculate the above assuming a coefficient of discharge of 0.96 and a nozzle efficiency of 0.92.
3430 mm2; 5310 mm2
Problem 4
A convergent-divergent nozzle expands air at 6.89 bar and 427 0C into a space at 1bar. The throat area of the nozzle is 650 mm2 and the exit area is 975 mm2. The exit velocity is found to be 680 m/s when the inlet velocity is negligible. Assuming that friction in the convergent portion is negligible, calculate:
(i)
The mass flow through the nozzle, stating whether the nozzle is underexpanding or overexpanding;
(ii)
The nozzle efficiency and the coefficient of velocity.
0.684 kg/s; underexpanding, p2 = 1.39 bar; 0.895, 0.946
Problem 5
Steam enters a convergent-divergent nozzle at 11 bar, dry saturated at a rate of 0.75 ks/s, and expands
pv
1.135 isentropically to 2.7 bar. Neglecting the inlet velocity, and assuming the expansion follows a law,
=
constant, calculate:
(i)
the area of the nozzle throat;
(ii)
the area of the nozzle exit.
474 mm2; 646 mm2
Problem 6 (Problem 9-117 from Thermodynamics - An_Engineering Approach Cengel & Boles)
A turbojet aircraft is flying with a velocity of 320 m/s at an altitude of 9150 m, where the ambient conditions are 32 kPa and 32°C. The pressure ratio across the compressor is
McConkey, page 325.
Problem 1
Calculate the throat and exit areas of a nozzle to expand air at a rate of 4.5 kg/s from 8.3 bar, 327 0C into a space at 1.38 bar. Neglect the inlet velocity and assume isentropic flow.
3290 mm2; 4840 mm2
Problem 2
It is required to produce a stream of helium at the rate of 0.1 kg/s travelling at sonic velocity at a temperature of 150C. Assume isentropic flow, negligible inlet velocity and a back pressure (= exit pressure) of 1.013 bar, calculate:
(i) the required inlet pressure and temperature;
(ii) The exit area of the nozzle.
Molar mass of helium is 4 kg/kmol, and = 1.66
2.077 bar; 1100C; 593 mm2
Problem 3
Recalculate the above assuming a coefficient of discharge of 0.96 and a nozzle efficiency of 0.92.
3430 mm2; 5310 mm2
Problem 4
A convergent-divergent nozzle expands air at 6.89 bar and 427 0C into a space at 1bar. The throat area of the nozzle is 650 mm2 and the exit area is 975 mm2. The exit velocity is found to be 680 m/s when the inlet velocity is negligible. Assuming that friction in the convergent portion is negligible, calculate:
(i)
The mass flow through the nozzle, stating whether the nozzle is underexpanding or overexpanding;
(ii)
The nozzle efficiency and the coefficient of velocity.
0.684 kg/s; underexpanding, p2 = 1.39 bar; 0.895, 0.946
Problem 5
Steam enters a convergent-divergent nozzle at 11 bar, dry saturated at a rate of 0.75 ks/s, and expands
pv
1.135 isentropically to 2.7 bar. Neglecting the inlet velocity, and assuming the expansion follows a law,
=
constant, calculate:
(i)
the area of the nozzle throat;
(ii)
the area of the nozzle exit.
474 mm2; 646 mm2
Problem 6 (Problem 9-117 from Thermodynamics - An_Engineering Approach Cengel & Boles)
A turbojet aircraft is flying with a velocity of 320 m/s at an altitude of 9150 m, where the ambient conditions are 32 kPa and 32°C. The pressure ratio across the compressor is