fluid_mechanics

588 Chapter 11 ■ Compressible Flow
E XAMPLE 11.3
Speed of Sound
GIVEN Consider the data in Table B.4. FIND Verify the speed of sound for air at 0 °C.
SOLUTION
In Table B.4, we find the speed of sound of air at 0 °C given as
331.4 ms. Assuming that air behaves as an ideal gas, we can calculate
the speed of sound from Eq. 11.36 as
c 2RTk
The value of the gas constant is obtained from Table 1.8 as
R 286.9 J1kg # K2
and the specific heat ratio is listed in Table B.4 as
k 1.401
By substituting values of R, k, and T into Eq. 1 we obtain
(1)
c 231286.92 J1kg # K241273.15 K211.4012
331.4 1Jkg2 1 2
Thus, since 1 Jkg 1 N # mkg 1 1kg # ms 2 2 # mkg
1 1ms2 2 , we obtain
c 331.4 ms
(Ans)
COMMENT The value of the speed of sound calculated with
Eq. 11.36 agrees very well with the value of c listed in Table B.4.
The ideal gas approximation does not compromise this result significantly.
11.3 Categories of Compressible Flow
Compressibility effects
are more important
at higher
Mach numbers.
In Section 3.8.1, we learned that the effects of compressibility become more significant as the Mach
number increases. For example, the error associated with using rV 2 2 in calculating the stagnation
pressure of an ideal gas increases at larger Mach numbers. From Fig. 3.24 we can conclude
that incompressible flows can only occur at low Mach numbers.
Experience has also demonstrated that compressibility can have a large influence on other
important flow variables. For example, in Fig. 11.2 the variation of drag coefficient with Reynolds
1.0
Ma = 1.2
2.0
3.0 1.5
0.9
4.5
1.1
0.8
1.0
0.7
0.9
0.6
0.7
C D
2 3 4 5 6 7 8 9
0.5
0.6
0.4
0.3
0.2
0.3
0.5
0.1
0
Re × 10 –5
F I G U R E 11.2 The variation of the drag coefficient
of a sphere with Reynolds number and Mach number.
(Adapted from Fig. 1.8 in Ref. 1 of Chapter 9.)