Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

840 | Thermodynamics

The critical-pressure ratio is determined from Table 17–2 (or Eq. 17–22) to

be P*/P 0 
0.5283.

(a) The back pressure ratio for this case is

which is greater than the critical-pressure ratio, 0.5283. Thus the exit plane

pressure (or throat pressure Pt) is equal to the back pressure in this case. That

is, Pt
Pb
0.7 MPa, and Pt/P 0 
0.670. Therefore, the flow is not choked.

From Table A–32 at Pt/P 0 
0.670, we read Mat
0.778 and Tt/T 0 
0.892.

The mass flow rate through the nozzle can be calculated from Eq. 17–24.

But it can also be determined in a step-by-step manner as follows:

Thus,

(b) The back pressure ratio for this case is

which is less than the critical-pressure ratio, 0.5283. Therefore, sonic condi-

tions exist at the exit plane (throat) of the nozzle, and Ma 
1. The flow is

choked in this case, and the mass flow rate through the nozzle can be calcu-

lated from Eq. 17–25:

since.

Discussion This is the maximum mass flow rate through the nozzle for the

specified inlet conditions and nozzle throat area.

kPa#m^2 > 2 kJ>kg
21000 kg>s

7.10 kg/s

 150  10 ^4 m^221 1045 kPa 2 

B

1.4

1 0.287 kJ>kg#K 21 884 K 2

a

2

1.4 1

b

2.4>0.8

m

#


A*P 0

B

k

RT 0

a

2

k 1

b

1 k 1 2>3 21 k 124

Pb

P 0

0.4 MPa

1.045 MPa

0.383

m

#


rtAtVt
 1 3.093 kg>m^32150  10 ^4 m^221 437.9 m>s 2 
6.77 kg/s

437.9 m>s

 1 0.778 2

B

1 1.4 21 0.287 kJ>kg#K 21 788.5 K2a

1000 m^2 >s^2

1 kJ>kg

b

Vt
Matct
Mat 2 kRTt

rt

Pt

RTt

700 kPa

1 0.287 kPa#m^3 >kg#K 21 788.5 K 2

3.093 kg>m^3

Tt
0.892T 0 
0.892 1 884 K 2 
788.5 K

Pb

P 0

0.7 MPa

1.045 MPa

0.670

EXAMPLE 17–6 Gas Flow through a Converging Nozzle

Nitrogen enters a duct with varying flow area at T 1 
400 K, P 1 
100 kPa,

and Ma 1 
0.3. Assuming steady isentropic flow, determine T 2 , P 2 , and Ma 2

at a location where the flow area has been reduced by 20 percent.

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