Modern Engineering Thermodynamics

676 CHAPTER 16: Compressible Fluid Flow
CRITICAL THINKING
Normal shock waves form as a result of a piling up of pressure waves into a strong compression wave front. A similar phenomenon
occurs as gravity waves in the ocean approach a beach. The front of each wave steepens as it approaches the
beach, but unlike shock waves it eventually topples over forming a breaker. Shock waves do not topple over, they continue
to grow in strength as their velocity increases. The strength of a normal shock wave is defined as the ratio of the pressure
increase across the shock to the original pressure, or (p y – p x )/p x . How would you define a similar strength for a gravity wave
in the ocean?
occurs at the exit plane of the nozzle and p exit = p E < p B . Finally, when p B /p os is below point d on Figure 16.21,
shock waves occur downstream from the nozzle and p exit = p E > p B .
If we apply the mass, energy, entropy, and linear momentum balances to the normal shock wave system shown
in Figure 16.22, we can relate the upstream (x) anddownstream(y) properties across the shock. Assuming a
steady state, steady flow, single-inlet, single-outlet, adiabatic, and aergonic system, the mass, energy, and linear
momentum rate balances give
but, since A x = A y = A in Figure 16.22,
Now, ρ = p/RT, so
Mass rate balance (MRB, SS, SF, SI, SO)
_m x = ρ x A x V x = _m y = ρ y A y V y
ρ x V x = ρ y V y
and
or
ρ x V x = p xV x
RT x
= kg 1/2
cp x V x kg c
= p x M x
kg c RT x RT x
1/2
kg c
ρ y V y = p y M y = ρ
RT x V x
y
x M x
p ffiffiffiffiffi = yM y
p ffiffiffiffi
(16.34)
T x
Energy rate balance (ERB, SS, SF, SI, SO, aergonic, adiabatic)
T y
h ox = h x + V 2 x /ð2g cÞ = h y + V 2 y /ð2g cÞ = h oy
Open system moving
with shock wave
Supersonic
M x > 1
p x , T x , ρ x , V x
x
y
Subsonic
M y < 1
p y , T y , ρ y , V y
FIGURE 16.22
A normal shock wave moving at supersonic velocity in a constant area adiabatic duct. The coordinate system here is fixed to the
shock wave.