Solution

12.43
Borgnakke and Sonntag
Consider an ideal air-standard cycle for a gas-turbine, jet propulsion unit, such as
that shown in Fig. 12.9. The pressure and temperature entering the compressor are
90 kPa, 290 K. The pressure ratio across the compressor is 14 to 1, and the turbine
inlet temperature is 1500 K. When the air leaves the turbine, it enters the nozzle
and expands to 90 kPa. Determine the velocity of the air leaving the nozzle.
Solution:
1
2 3
BURNER
COMPR. TURBINE
4
NOZ
5
T
2
1
P
3
4
5
P = 90 kPa
C.V. Compressor: Reversible and adiabatic s 2 = s 1 From Eq.8.25, 8.32
T 2 = T 1⎝ ⎜ ⎛
k-1
P2 P1 ⎞ k 0.2857
⎟ = 290 (14) = 616.4 K
⎠
w C = h 2 - h 1 ≈ C P0 (T 2 – T 1) = 1.004 (616.4 – 290) = 327.7 kJ/kg
C.V. Turbine: w T = h 3 - h 4 = w C and s 4 = s 3 ⇒
T 4 = T 3 - w C/C P0 = 1500 - 327.7/1.004 = 1173.6 K
C.V. Nozzle: s 5 = s 4 = s 3 so from Eq.8.32
T 5 = T 3 ⎝ ⎜ ⎛
k-1
P5 P3 Now the energy equation
⎞ k
⎟ = 1500 ⎜
⎠ ⎝ ⎛ 90 ⎞
1260
⎟
⎠
0.2857
= 705.7 K
(1/2)V 5 2 = h4 - h 5 ≈ C P0 (T 4 – T 5) = 1.004 (1173.6 – 705.7) = 469.77 kJ/kg
⇒ V 5 = 2 × 1000 × 469.77 = 969 m/s
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