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

at constant velocity in still air may be different at different locations
(Fig. 17–10).
Fluid flow regimes are often described in terms of the flow Mach number.
The flow is called sonicwhen Ma
1,subsonicwhen Ma 1,supersonic
when Ma 1,hypersonicwhen Ma 1, and transonicwhen Ma
1.

Chapter 17 | 829

AIR V = 320 m/s

200 K

300 K

AIR V = 320 m/s

Ma = 0.92

Ma = 1.13

FIGURE 17–10

The Mach number can be different at

different temperatures even if the

velocity is the same.

Diffuser

V = 200 m/s

T = 30°C

AIR

FIGURE 17–11

Schematic for Example 17–2.

1400

Stagnation

region:

1400 kPa

200 °C

CO 2

1000

3 kg/s

767 200

P, kPa

m⋅

FIGURE 17–12

Schematic for Example 17–3.

EXAMPLE 17–2 Mach Number of Air Entering a Diffuser

Air enters a diffuser shown in Fig. 17–11 with a velocity of 200 m/s. Deter-

mine (a) the speed of sound and (b) the Mach number at the diffuser inlet

when the air temperature is 30°C.

Solution Air enters a diffuser with a high velocity. The speed of sound and

the Mach number are to be determined at the diffuser inlet.

Assumptions Air at specified conditions behaves as an ideal gas.

Properties The gas constant of air is R
0.287 kJ/kg · K, and its specific

heat ratio at 30°C is 1.4 (Table A–2a).

Analysis We note that the speed of sound in a gas varies with temperature,

which is given to be 30°C.

(a) The speed of sound in air at 30°C is determined from Eq. 17–11 to be

(b) Then the Mach number becomes

Discussion The flow at the diffuser inlet is subsonic since Ma 1.

Ma

V

c

200 m>s

349 m>s

0.573

c
 2 kRT


B

1 1.4 21 0.287 kJ>kg#K 21 303 K2a

1000 m^2 >s^2

1 kJ>kg

b
349 m/s

17–3 ■ ONE-DIMENSIONAL ISENTROPIC FLOW

During fluid flow through many devices such as nozzles, diffusers, and tur-
bine blade passages, flow quantities vary primarily in the flow direction
only, and the flow can be approximated as one-dimensional isentropic flow
with good accuracy. Therefore, it merits special consideration. Before pre-
senting a formal discussion of one-dimensional isentropic flow, we illustrate
some important aspects of it with an example.

EXAMPLE 17–3 Gas Flow through a Converging–Diverging Duct

Carbon dioxide flows steadily through a varying cross-sectional-area duct

such as a nozzle shown in Fig. 17–12 at a mass flow rate of 3 kg/s. The car-

bon dioxide enters the duct at a pressure of 1400 kPa and 200°C with a low

velocity, and it expands in the nozzle to a pressure of 200 kPa. The duct is

designed so that the flow can be approximated as isentropic. Determine the

density, velocity, flow area, and Mach number at each location along the

duct that corresponds to a pressure drop of 200 kPa.

Solution Carbon dioxide enters a varying cross-sectional-area duct at speci-

fied conditions. The flow properties are to be determined along the duct.