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

decelerated in a subsonic diffuser, which has a flow area that increases in

the flow direction, as shown in Fig. 17–17.

Property Relations for Isentropic Flow

of Ideal Gases

Next we develop relations between the static properties and stagnation proper-

ties of an ideal gas in terms of the specific heat ratio kand the Mach number

Ma. We assume the flow is isentropic and the gas has constant specific heats.

The temperature Tof an ideal gas anywhere in the flow is related to the

stagnation temperature T 0 through Eq. 17–4:

or

Noting that cp
kR/(k1),c^2 
kRT, and Ma 
V/c, we see that

Substituting yields

(17–18)

which is the desired relation between T 0 and T.

T 0

T

 1 a

k 1

2

bMa^2

V^2

2 cpT

V^2

23 kR>1k 124 T

a

k 1

2

b

V^2

c^2

a

k 1

2

bMa^2

T 0

T

 1 

V^2

2 cpT

T 0 
T

V^2

2 cp

834 | Thermodynamics

Subsonic nozzle

(a) Subsonic flow

Ma< 1

Supersonic diffuser

Ma> 1

Supersonic nozzle

Ma> 1

Subsonic diffuser

Ma< 1

(b) Supersonic flow

P decreases

V increases

Ma increases

T decreases

r decreases

P decreases

V increases

Ma increases

T decreases

r decreases

P increases

V decreases

Ma decreases

T increases

r increases

P increases

V decreases

Ma decreases

T increases

FIGURE 17–17 r increases

Variation of flow properties in

subsonic and supersonic nozzles and

diffusers.

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