Thermodynamics
Example 1
Nozzle Flow - Steam Steam at 1.5 bar and 150 deg C enters a nozzle at 10 m/s and exits at 1 bar. Assuming the flow is reversible and adiabatic, determine the exit temperature and velocity. If the exit nozzle area is 0.001 m2, evaluate the mass flow rate of the steam through the nozzle. P1 = 1.5 bar T1 = 90 deg C V1 = 10 m/s A2 = 0.001 m2
P2 =1 bar T2 = ? V2 = ? mdot = ?
V2 = sqrt(V1*V1+2*(h1-h2)) mdot = rho*A2*V2 = A2*V2/v2 T2
382.60 m/s 0.22 kg/s 111.81 degC
Superheated steam at nozzle entry T1 150 deg C P1 1.5 bar s1 7.420 kJ/kg K h1 2773 kJ/kg K V1 10 m/s P2 A2 1 bar 0.001 m2
At Nozzle exit P2 = 1 bar Rev & Adiabatic s1 = s2 = 7.420 kJ/kg K h2 (Superheated because s2 > sg2 (7.359)
s 7.360 7.614 7.420 s 7.360 7.614 7.420 s 7.360 7.614 7.420
h 2676 2777 2699.86 v 1.696 1.937 1.753 T 100 150 111.81
v2
T2
Example 2
Nozzle Flow - Air Air enters a nozzle at 1.5 bar and 90 deg C at a velocity of 10 m/s and exits the nozzle at 1 bar. Assuming the flow is reversible and adiabatic, determine the exit temperature and velocity. If the exit nozzle area is 0.001 m2, evaluate the mass flow rate of the air through the nozzle. P1 = 1.5 bar T1 = 90 deg C V1 = 10 m/s A2 = 0.001 m2
P2 =1 bar T2 = ? V2 = ? mdot = ? R Cp Cv gama = Cp/Cv
0.287 kJ/kg K 1.005 kJ/kg K 0.718 kJ/kg K 1.40
(gama-1)/gama = exp T2 = T1*(P2/P1)^exp process for reversible and adiabatic
0.29
323.31 K 50.31 deg C 282.62 m/s 1.50 0.30 kg/s 0.93 m3/kg
T1 P1 V1 P2 A2
V2 = sqrt(V1*V1+2*Cp*(T1-T2)) P1/P2 mdot = rho*A2*V2 = A2*V2/v2 v2 = R*T2/P2
90 363 1.5 10
deg C K bar m/s
1 bar 0.001 m2
Example 3
Cengel_5_30_Nozzle Flow - Air Air enters an adiabatic nozzle steadily at 3 bar and 200 deg C at a velocity of 30 m/s and exits the nozzle at 1 bar and 180 m/s. The inlet area of the nozzle is is 80 cm2. Determine (a) the mass flow rate through the nozzle, (b) the exit temperatureof the air and (c) the the exit area of the nozzle.
mdot =
Nozzle Flow - Steam Steam at 1.5 bar and 150 deg C enters a nozzle at 10 m/s and exits at 1 bar. Assuming the flow is reversible and adiabatic, determine the exit temperature and velocity. If the exit nozzle area is 0.001 m2, evaluate the mass flow rate of the steam through the nozzle. P1 = 1.5 bar T1 = 90 deg C V1 = 10 m/s A2 = 0.001 m2
P2 =1 bar T2 = ? V2 = ? mdot = ?
V2 = sqrt(V1*V1+2*(h1-h2)) mdot = rho*A2*V2 = A2*V2/v2 T2
382.60 m/s 0.22 kg/s 111.81 degC
Superheated steam at nozzle entry T1 150 deg C P1 1.5 bar s1 7.420 kJ/kg K h1 2773 kJ/kg K V1 10 m/s P2 A2 1 bar 0.001 m2
At Nozzle exit P2 = 1 bar Rev & Adiabatic s1 = s2 = 7.420 kJ/kg K h2 (Superheated because s2 > sg2 (7.359)
s 7.360 7.614 7.420 s 7.360 7.614 7.420 s 7.360 7.614 7.420
h 2676 2777 2699.86 v 1.696 1.937 1.753 T 100 150 111.81
v2
T2
Example 2
Nozzle Flow - Air Air enters a nozzle at 1.5 bar and 90 deg C at a velocity of 10 m/s and exits the nozzle at 1 bar. Assuming the flow is reversible and adiabatic, determine the exit temperature and velocity. If the exit nozzle area is 0.001 m2, evaluate the mass flow rate of the air through the nozzle. P1 = 1.5 bar T1 = 90 deg C V1 = 10 m/s A2 = 0.001 m2
P2 =1 bar T2 = ? V2 = ? mdot = ? R Cp Cv gama = Cp/Cv
0.287 kJ/kg K 1.005 kJ/kg K 0.718 kJ/kg K 1.40
(gama-1)/gama = exp T2 = T1*(P2/P1)^exp process for reversible and adiabatic
0.29
323.31 K 50.31 deg C 282.62 m/s 1.50 0.30 kg/s 0.93 m3/kg
T1 P1 V1 P2 A2
V2 = sqrt(V1*V1+2*Cp*(T1-T2)) P1/P2 mdot = rho*A2*V2 = A2*V2/v2 v2 = R*T2/P2
90 363 1.5 10
deg C K bar m/s
1 bar 0.001 m2
Example 3
Cengel_5_30_Nozzle Flow - Air Air enters an adiabatic nozzle steadily at 3 bar and 200 deg C at a velocity of 30 m/s and exits the nozzle at 1 bar and 180 m/s. The inlet area of the nozzle is is 80 cm2. Determine (a) the mass flow rate through the nozzle, (b) the exit temperatureof the air and (c) the the exit area of the nozzle.
mdot =