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Modern Engineering Thermodynamics

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16.5 Converging-Diverging Flows 663<br />

M < 1<br />

Fan<br />

motor<br />

Nozzle<br />

throat<br />

M* = 1<br />

Diffuser<br />

throat<br />

M* = 1<br />

M < 1 M>1<br />

M< 1<br />

FIGURE 16.12<br />

A supersonic wind tunnel design.<br />

and<br />

Convergingdiverging<br />

nozzle<br />

Supersonic<br />

test section<br />

Convergingdiverging<br />

diffuser<br />

1/ðk−1Þ<br />

ρ 2<br />

= ρ os (16.20)<br />

k + 1<br />

When a subsonic nozzle and a supersonic nozzle are joined at their throats, they form a converging-diverging<br />

nozzle that can be used to generate supersonic velocities. Also, connecting a supersonic diffuser to a subsonic<br />

diffuser forms a converging-diverging diffuser that can be used to decelerate a supersonic flow and recover its<br />

kinetic energy by converting it into pressure. These two converging-diverging geometries are often combined in<br />

the design of a supersonic wind tunnel, as shown in Figure 16.12. Note that the diverging part of the nozzle<br />

cannot become supersonic until the throat becomes critical at a Mach number of 1.0. This is called choked flow<br />

and is discussed in the next section.<br />

EXAMPLE 16.6<br />

A converging-diverging nozzle is attached via a valve to a pipe holding compressed air at 1.00 MPa and 20.0°C. The valve is<br />

opened and the air passes through the nozzle and into the atmosphere. Assuming isentropic flow throughout, determine<br />

a. The exit Mach number.<br />

b. The exit temperature.<br />

c. The exit velocity.<br />

d. The pressure at the throat of the nozzle.<br />

e. The temperature at the throat of the nozzle.<br />

Solution<br />

First, draw a sketch of the system (Figure 16.13).<br />

1 MPa<br />

Converging-diverging<br />

nozzle<br />

p = p atm = 0.1013 MPa<br />

20°C<br />

Valve<br />

Pipe<br />

FIGURE 16.13<br />

Example 16.6.<br />

(Continued )

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