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

17–4 ■ ISENTROPIC FLOW THROUGH NOZZLES

Converging or converging–diverging nozzles are found in many engineering

applications including steam and gas turbines, aircraft and spacecraft

propulsion systems, and even industrial blasting nozzles and torch nozzles.

In this section we consider the effects of back pressure(i.e., the pressure

applied at the nozzle discharge region) on the exit velocity, the mass flow

rate, and the pressure distribution along the nozzle.

Converging Nozzles

Consider the subsonic flow through a converging nozzle as shown in

Fig. 17–20. The nozzle inlet is attached to a reservoir at pressure Prand

temperature Tr. The reservoir is sufficiently large so that the nozzle inlet

velocity is negligible. Since the fluid velocity in the reservoir is zero and

the flow through the nozzle is approximated as isentropic, the stagnation

pressure and stagnation temperature of the fluid at any cross section

through the nozzle are equal to the reservoir pressure and temperature,

respectively.

836 | Thermodynamics

EXAMPLE 17–4 Critical Temperature and Pressure in Gas Flow

Calculate the critical pressure and temperature of carbon dioxide for the flow

conditions described in Example 17–3 (Fig. 17–19).

Solution For the flow discussed in Example 17–3, the critical pressure and

temperature are to be calculated.

Assumptions 1 The flow is steady, adiabatic, and one-dimensional. 2 Carbon

dioxide is an ideal gas with constant specific heats.

Properties The specific heat ratio of carbon dioxide at room temperature is

k
1.289 (Table A–2a).

Analysis The ratios of critical to stagnation temperature and pressure are

determined to be

Noting that the stagnation temperature and pressure are, from Example

17–3, T 0 
473 K and P 0 
1400 kPa, we see that the critical temperature

and pressure in this case are

Discussion Note that these values agree with those listed in Table 17–1, as

expected. Also, property values other than these at the throat would indicate

that the flow is not critical, and the Mach number is not unity.

P*
0.5477P 0 
 1 0.5477 21 1400 kPa 2 
767 kPa

T*
0.8737T 0 
 1 0.8737 21 473 K 2 
413 K

P*

P 0

a

2

k 1

b

k>1k 12


a

2

1.289 1

b

1.289>11.289 12


0.5477

T*

T 0

2

k 1

2

1.289 1

0.8737

T*

P*

= 473 K

= 1.4 MPa

CO 2

T 0

P 0

FIGURE 17–19

Schematic for Example 17–4.

x

Lowest exit

pressure

P/P 0

Reservoir P

e

x

P*

Vr= 0

0

1

P 0

Pb =P*

Pb <P*

5 Pb =0

4

3

2

1

Pb >P*

Pb =P 0

Pb

(Back

pressure)

Pr = P 0

Tr = T 0

FIGURE 17–20

The effect of back pressure on the

pressure distribution along a

converging nozzle.

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