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

Chapter 17 | 871

Analysis We denote the entrance, throat, and exit states by 1, t, and 2,

respectively, as shown in Fig. 17–60.

(a) Since the inlet velocity is negligible, the inlet stagnation and static states

are identical. The ratio of the exit-to-inlet stagnation pressure is

It is much smaller than the critical-pressure ratio, which is taken to be

P*/P 01 
0.546 since the steam is superheated at the nozzle inlet. There-

fore, the flow surely is supersonic at the exit. Then the velocity at the throat

is the sonic velocity, and the throat pressure is

At the inlet,

Also, at the throat,

Then the throat velocity is determined from Eq. 17–3 to be

The flow area at the throat is determined from the mass flow rate relation:

At state 2s,

The enthalpy of the steam at the actual exit state is (see Chap. 7)

Therefore,

Then the exit velocity and the exit area become

A 2 

m#v 2

V 2

1 2.5 kg>s 21 0.67723 m^3 >kg 2

929.8 m>s

18.21 10 ^4 m^2 
18.21 cm^2

V 2 
 221 h 01 h 22 


B

321 3248.42816.1 2 kJ>kg4a

1000 m^2 >s^2

1 kJ>kg

b
929.8 m>s

P 2 
300 kPa

h 2 
2816.1 kJ>kg

f¬

v 2 
0.67723 m^3 >kg

s 2 
7.2019 kJ>kg#K

0.93

3248.4h 2

3248.42783.6

¡ h 2 
2816.1 kJ>kg

hN

h 01 h 2

h 01 h 2 s

P 2 s
P 2 
300 kPa

s 2 s
s 1 
7.1292 kJ>kg#K

f h 2 s
2783.6 kJ>kg

At

m#vt

Vt

1 2.5 kg/s 21 0.2420 m^3 /kg 2

585.8 m/s

10.33 10 ^4 m^2 
10.33 cm^2

Vt
 221 h 01 ht 2 


B

321 3248.43076.8 2 kJ/kg4a

1000 m^2 >s^2

1 kJ>kg

b
585.8 m/s

Pt
1.09 MPa

st
7.1292 kJ>kg#K

f¬

ht
3076.8 kJ>kg

vt
0.24196 m^3 >kg

P 1 
P 01 
2 MPa

T 1 
T 01 
400°C

f¬

h 1 
h 01 
3248.4 kJ>kg

s 1 
st
s 2 s
7.1292 kJ>kg#K

Pt
0.546P 01 
 1 0.546 21 2 MPa 2 
1.09 MPa

P 2

P 01

300 kPa

2000 kPa

0.15

s

h

1

P 2 = 30

0 kP

a

2

2 s

t

Pt

P 1 =^

P 01

= 2 MPa

T 1 = 400°C

P 1 = 2 MPa

V 1 ≅ 0

STEAM

Throat

m· = 2.5 kg/s

hN = 93%

FIGURE 17–60

Schematic and h-sdiagram for

Example 17–16.

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