across the normal shock (s 2 s 1 )/Rversus Ma 1 is shown in Fig. 17–34.
Since the flow across the shock is adiabatic and irreversible, the second law
requires that the entropy increase across the shock wave. Thus, a shock
wave cannot exist for values of Ma 1 less than unity where the entropy
change would be negative. For adiabatic flows, shock waves can exist only
for supersonic flows, Ma 1 1.Chapter 17 | 849FIGURE 17–33
Schlieren image of the blast wave
(expanding spherical normal shock)
produced by the explosion of a
firecracker detonated inside a metal can
that sat on a stool. The shock expanded
radially outward in all directions at a
supersonic speed that decreased with
radius from the center of the explosion.
The microphone at the lower right
sensed the sudden change in pressure
of the passing shock wave and
triggered the microsecond flashlamp
that exposed the photograph.
Photo by G. S. Settles, Penn State University. Used
by permission.0Impossible
Subsonic flow
before shockMa 1 = 1Supersonic flowMa 1
before shocks 2 – s 1 < 0s 2 – s 1 > 0(s 2 s 1 )/RFIGURE 17–34
Entropy change across the normal
shock.EXAMPLE 17–8 The Point of Maximum Entropy
on the Fanno LineShow that the point of maximum entropy on the Fanno line (point bof Fig.
17–31) for the adiabatic steady flow of a fluid in a duct corresponds to the
sonic velocity, Ma 1.Solution It is to be shown that the point of maximum entropy on the Fanno
line for steady adiabatic flow corresponds to sonic velocity.
Assumptions The flow is steady, adiabatic, and one-dimensional.
Analysis In the absence of any heat and work interactions and potential
energy changes, the steady-flow energy equation reduces toDifferentiating yieldsFor a very thin shock with negligible change of duct area across the shock, the
steady-flow continuity (conservation of mass) equation can be expressed asrVconstantdhV dV 0hV^2
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