12.1: PROBLEM DEFINITION
Situation:
The speed of sound in an ideal gas _______. (Select all that are correct):
a. depends upon √Twhere Tis absolute temperature
b. depends upon √Twhere Tis temperature in ◦C
c. depends upon √k,wherek=cp
cv,aratioofspecific heats for a given gas
SOLUTION
1
12.2: PROBLEM DEFINITION
Part a.
Situation:
Speed of sound in air is 340 m/s
Find:
Speed in miles per hour.
SOLUTION
This requires a unit conversion.
Part b.
Situation:
4 seconds between seeing lightening and hearing thunder when T=50oF….
Find:
Distance to lightning strike.
Properties:
Table A.2 (EFM 10e), Rair =1716lbf-ft/slugs-R
SOLUTION
Thunder travels at the speed of sound. The speed of sound in a gas is given by:
Therefore, the distance for this case is:
2
12.3: PROBLEM DEFINITION
Situation:
The Mach number _______. (Select all that are correct).
a. is the ratio V/c,wherec=specificheat
b. is the ratio V/c,wherec=the speed of sound
c. depends on the velocity, V, of the moving body relative to the fluid flow
d. has a magnitude of M<1for subsonic flow
e. has a magnitude of M>1for supersonic flow
SOLUTION
3
12.4: PROBLEM DEFINITION
Situation: Investigate cruise Mach number of conventional airliners and possible re-
gions of supersonic flow.
SOLUTION Nominally commercial transport aircraft flyataMachnumberof0.8
4
12.5: PROBLEM DEFINITION
Situation: Satellite re-entry of earth’s atmosphere at -60oC…
Find:Machnumber
Properties:TableA.2(EFM10e),Rair =287J/kg-K
SOLUTION Orbital velocity
Speed of sound
Mach number
5
12.6: PROBLEM DEFINITION
Situation: A sound wave travels in methane at −5◦C.
Find: Speed of wave.
Properties:TableA.2(EFM10e),Rmethane =513J/kg-K, k=1.31
SOLUTION Speed of sound in a gas
6
12.7: PROBLEM DEFINITION
Situation: A sound wave travels in helium at 45 ◦C.
Find: Speed of wave.
Properties:TableA.2(EFM10e),RHe =2077J/kg-K, k=1,66
SOLUTION Speed of sound in a gas
7
12.8: PROBLEM DEFINITION
Situation: A sound wave travels in hydrogen at 38 ◦F.
Find: Speed of wave.
Properties:TableA.2(EFM10e),RH2=24,677 Ft-lbf/slug-R, k=1.41
SOLUTION Speed of sound
8
12.9: PROBLEM DEFINITION
Situation: A sound wave travels in helium and another in nitrogen both at 20 ◦C.
Find:Difference in speed of sound.
Properties: Table A.2 (EFM 10e), RHe =2077J/kg-K, k=1.66,R
N2=297J/kg-K,
k=1.40
SOLUTION Speed of sound
9
12.10: PROBLEM DEFINITION
Situation: A sound wave travels in an ideal gas.
Find: Speed of sound for an isothermal process.
SOLUTION
If isothermal, T=const.
10
12.11: PROBLEM DEFINITION
Situation: The relationship between pressure and density for sound travelling through
afluid is
p−p0=Evln(ρ/ρ0)
Find: Speed of sound in water.
Properties:EV=2.2GPa, ρ=1000kg/m3.
SOLUTION
11
12.12: PROBLEM DEFINITION
Situation:Anaircraftflying in air at 30oCatMach1.6.
Find: Surface temperature.
Properties:TableA.2(EFM10e),dataforair,k=1.4
SOLUTION Total temperature will develop at exposed surface.Total temperature
12
12.13: PROBLEM DEFINITION
Situation:Afighter is flying at Mach 3 though air at −20 ◦C.
Find: Temperature on nose.
Properties:FromTableA.2(EFM10e),k=1.4
SOLUTION Total temperature will develop at exposed surface. Total temperature
13
12.14: PROBLEM DEFINITION
Situation:Anaircraftisflying at Mach 1.8 through air at 10000 m,30.5kPa,and
−44 ◦C.
Find: (a) Speed of aircraft.
(b) Total temperature.
(c) Speed for M=1.
Properties:FromTableA.2(EFM10e),k=1.4,R
air =287J/kg-K
SOLUTION Speed of sound (at 10,000 m)
a) Speed
b) Total temperature
c) Speed for Mach number=1
14
12.15: PROBLEM DEFINITION
Situation: An airplane is travelling at 850 km/hr at sea level where temperature is
10 ◦C.
Find: Speed of aircraft with same Mach number at altitude where T=−50 ◦C.
Properties:FromTableA.2(EFM10e),k=1.4,R
air =287J/kg-K
PLAN Apply the Mach number equation and the speed of sound equation.
SOLUTION At sea level
Speed of sound (sea level)
Mach number(sea level)
Speed of sound (at altitude)
Mach number (at altitude)
15
12.16: PROBLEM DEFINITION
Situation:Anaircraftflying at M=0.95 through air at 10,000 m where T=-44oCand
p=30 kPa, abs. Lift coefficient is 0.05.
Find:Wingloading.
SOLUTION Kinetic pressure
Lift force
16
12.17: PROBLEM DEFINITION
Situation: Early passenger aircraft flew at 230 mph at 15,000 ft.
Find: Importance of compressible flow effects.
SOLUTION Compressible flow effects not important for M<0.3.Temperature de–
creases at 5.87 K/km. An altitude of 15,000 ft corresponds to 4,570 m so temperature
drop would be 5.87×4.57 = 26.8oC. The absolute temperature would be 246 K. The
speed of sound is
The aircraft speed is
17
12.18: PROBLEM DEFINITION
Situation:Difference between total and stagnation pressure.
SOLUTION Total pressure is the pressure resulting when a flow is brought to
18
12.19: PROBLEM DEFINITION
Situation: An object immersed in a 250 m/s airflow at 200 kPa, abs and 20oC.
Find: (a) Pressure.
(b) Temperature at stagnation point.
Properties:FromTableA.2(EFM10e),k=1.4,R
air =287J/kg-K
SOLUTION Speed of sound
Mach number
Total properties
Temp erature
Pressure
19
12.20: PROBLEM DEFINITION
Situation:Anairflow with Mach number of 0.85 through a 60 cm2-conduit with
360 kPa absolute pressure and total temperature of 10 ◦C.
Find:Massflow rate through conduit.
Properties:FromTableA.2(EFM10e),k=1.4,R
air =287J/kg-K
PLAN Apply the flow rate equation, the ideal gas law, Mach number, speed of
sound, and the total properties equations.
SOLUTION Total temperature equation
Total pressure equation
Speed of sound
Velocity
Ideal gas law