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

critical ratio. Also illustrated on this figure is the effect of back pressure on

the nozzle exit pressure Pe. We observe that

To summarize, for all back pressures lower than the critical pressure P*,

the pressure at the exit plane of the converging nozzle Peis equal to P*, the

Mach number at the exit plane is unity, and the mass flow rate is the maxi-

mum (or choked) flow rate. Because the velocity of the flow is sonic at the

throat for the maximum flow rate, a back pressure lower than the critical

pressure cannot be sensed in the nozzle upstream flow and does not affect

the flow rate.

The effects of the stagnation temperature T 0 and stagnation pressure P 0 on

the mass flow rate through a converging nozzle are illustrated in Fig. 17–22

where the mass flow rate is plotted against the static-to-stagnation pressure

ratio at the throat Pt/P 0. An increase in P 0 (or a decrease in T 0 ) will increase

the mass flow rate through the converging nozzle; a decrease in P 0 (or an

increase in T 0 ) will decrease it. We could also conclude this by carefully

observing Eqs. 17–24 and 17–25.

A relation for the variation of flow area Athrough the nozzle relative to

throat area A* can be obtained by combining Eqs. 17–24 and 17–25 for the

same mass flow rate and stagnation properties of a particular fluid. This

yields

(17–26)

Table A–32 gives values of A/A* as a function of the Mach number for air

(k
1.4). There is one value of A/A* for each value of the Mach number,

but there are two possible values of the Mach number for each value of

A/A*—one for subsonic flow and another for supersonic flow.

A

A*

1

Ma

ca

2

k 1

ba 1 

k 1

2

Ma^2 bd

1 k 1 2> 3 21 k 124

Pe
e

Pb for PbP*

P* for Pb 6 P*

838 | Thermodynamics

0

Pt

Decrease in ,

P* 1.0

P 0

m

P 0

P 0

P 0 , T 0

increase in T 0 ,

or both

Increase in ,P 0

decrease inT 0 ,

or both

Mat = 1 Mat< 1

⋅

FIGURE 17–22

The variation of the mass flow rate

through a nozzle with inlet stagnation

properties.

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