# Aerodynamics Questions and Answers – The Basic Normal Shock Equations – 2

This set of Aerodynamics Objective Questions & Answers focuses on “The Basic Normal Shock Equations – 2”.

1. For a non-perfect gas, if we double the pressure while keeping the temperature same, the speed of sound remains the same.
a) False
b) True

Explanation: For a non-perfect gas, the speed of sound is a pressure of temperature and pressure (or density). And hence, by changing the pressure, while keeping the temperature constant, speed of sound changes.

2. For a perfect gas, if we half the density, keeping the temperature same the speed of sound changes. This is due to the change in pressure.
a) True
b) False

Explanation: The given statement is false. For a perfect gas, the speed of sound is a pressure of temperature only. And hence, by changing pressure or density but keeping the temperature same, speed of sound will not change.

3. The isothermal compressibility is given as___________
a) Same as isentropic compressibility
b) $$\frac {1}{p}$$
c) $$\frac {1}{\gamma p}$$
d) $$\frac {\rho }{p}$$

Explanation: The isothermal compressibility differs from the isentropic compressibility by a factor of gamma. The isothermal compressibility is given as τt=$$\frac {1}{p}$$ while the isentropic compressibility is given as τs=$$\frac {1}{\gamma p}$$.

4. Which is not the correct reason for sound of speed being higher in helium than in air at the same temperature?
a) γ for helium is higher than air
b) Gas constant is same for both
c) Helium is lighter than air
d) R for helium is much larger than for air

Explanation: The sound of speed depends on gamma, T and the gas constant R for the respective gas. In case of helium and air, the gamma for helium is higher than air. Also, helium is lighter than air thus, R for helium being higher. This gives, at the same temperature, speed of sound more in helium than air.

5. The correct statement for a point where the speed of sound is a, is_______
a) a* is the stagnation speed of sound
b) a* is the maximum speed of sound
c) a0 is the characteristic speed of sound
d) a0 is the stagnation speed of sound

Explanation: For a point in the flow, where the speed of sound is a, a0 is the stagnation speed of sound associated with that point. While a* is the sonic characteristic value associated with that same point. None of these is the maximum speed of sound in the flow.
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6. The incorrect relation for properties associated with the flow, for a point in the flow where the speed of sound is a, is_______
a) $$\frac {\gamma +1}{2(\gamma -1)}$$ a*2=$$\frac {a_0^2}{\gamma -1}$$≠const
b) $$\frac {\gamma +1}{2(\gamma -1)}$$ a*2=const
c) $$\frac {a_0^2}{\gamma -1}$$=const
d) $$\frac {\gamma +1}{2(\gamma -1)}$$ a*2=$$\frac {a_0^2}{\gamma -1}$$=const

Explanation: The two properties, a* and a0, of the flow are related to each other by the relation: $$\frac {\gamma +1}{2(\gamma -1)}$$ a*2=$$\frac {a_0^2}{\gamma -1}$$. These two (a* and a0) are defined quantities and are constant at a point in the flow. Thus, the correct relation is $$\frac {\gamma +1}{2(\gamma -1)}$$ a*2=$$\frac {a_0^2}{\gamma -1}$$=const, since gamma is also a constant.

7. Select the incorrect statement for the properties concerned with a flow.
a) a* and a0 are constant at a point
b) a* and a0 are constant along the streamline for an adiabatic, inviscid, steady flow
c) a* and a0 are constant along the entire flow for an adiabatic, inviscid, steady flow
d) a* and a0 are related but not equal

Explanation: a* and a0 are the defined properties of the flow, constant at a point. They are related to each other but not same. For an adiabatic, inviscid, steady flow they are constant along the streamline. And if all the streamlines are coming from same uniform free-stream, they are constant along the entire flow.

8. For a calorically perfect gas, the ratio of stagnation to static temperature depends upon_______
a) γ
b) γ , M
c) M
d) R, M

Explanation: The stagnation and static temperatures for a calorically perfect gas are related with the equation $$\frac {T_0}{T}$$=1+$$\frac {\gamma -1}{2}$$M2. Thus, it is clearly seen that this ratio depends on the gamma and the Mach number in the medium. It’s a very important relationship.

9. The definitions of P0 and ρ0 involve______
a) Isothermal compression
b) Isentropic compression
d) Any process gives the same value

Explanation: The defined properties of the flow P0 and ρ0 involve isentropic compression, which is adiabatic and reversible both. These properties are the values of the flow parameters when the flow is isentropically compressed to zero velocity, at a point with properties P and ρ.

10.The properties of a flow with subscript * denotes M=1. Which of these is the correct ratio for a flow with gamma= 1.4?
a) $$\frac {T^*}{T_0}$$=0.528
b) $$\frac {P^*}{P_0}$$=0.833
c) $$\frac {\rho ^*}{\rho_0}$$=0.634

Explanation: The defined flow properties are related to each other with relations involving only Mach number and gamma. Hence, when these two values are given, the ratios can be calculated. These are important ratios and for M=1 and gamma=1.4 the values are $$\frac {T^*}{T_0}$$=0.833, $$\frac {P^*}{P_0}$$=0.528, $$\frac {\rho ^*}{\rho_0}$$=0.634

11. The characteristic Mach number is constant for a given value of temperature and gamma.
a) False
b) True

Explanation: The defined M* or the characteristic Mach number depends upon the Mach number, for any given gamma. It changes if the Mach number is changed, which changes by changing the flow speed at any temperature. Hence, the given statement is false.

12. The characteristic Mach number and Mach number are related. Which of these is not correct?
a) M=1, M*=1
b) M<1, M*<1
c) M<1, M*<1
d) M→∞, M*→0

Explanation: The characteristic Mach number and the Mach number behave almost in a similar pattern. The only difference if when the Mach number tends to infinity, the characteristic Mach number tends to a finite value. This finite value depends only on gamma is never zero.

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