Aircraft Performance Questions and Answers – Measurement of Mach Number

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This set of Aircraft Performance Multiple Choice Questions & Answers (MCQs) focuses on “Measurement of Mach Number”.

1. What is the formula for mach number?
a) M=$$\frac{V}{a}$$
b) M=$$\frac{a}{V}$$
c) V=$$\frac{a}{M}$$
d) a=$$\frac{M}{V}$$

Explanation: The formula for mach number is M=$$\frac{V}{a}$$ where M=mach number, V=velocity, a=speed of sound. There is no unit for mach number as it is a ratio of speed of the object to the speed of sound in the surrounding air.

2. What is the mach number of an aircraft flying with a speed of 450m/s at a temperature of 290 K?
a) 1.318
b) 2.045
c) 3.214
d) 0.235

Explanation: The answer is 1.318. Given T=290K , V= 450m/s. We know γ of air=1.4 and R=287 J/kg-K.
From the formula-M=$$\frac{V}{a}$$ where a=$$\sqrt{\gamma RT}$$
On substituting the values to find “a”,
we have a=$$\sqrt{1.2*287*290}$$
a=341.35m/s.
Now substituting the value of “a” in the formula=$$\frac{V}{a}$$,
we get M=$$\frac{450}{341.35}$$
M=1.318.

3. Which of the following is the correct relation for mach number?
a) M=V$$\sqrt{\frac{\rho}{\gamma P}}$$
b) V=$$\frac{a}{M}$$
c) M=V$$\sqrt{\frac{P}{\gamma\rho}}$$
d) M=V$$\sqrt{\frac{\gamma p}{\rho}}$$

Explanation: M=V$$\sqrt{\frac{\rho}{\gamma P}}$$ is the correct relation for mach number in terms of pressure and density. In M=V$$\sqrt{\frac{\rho}{\gamma P}}$$, M=mach number, V=velocity , ρ=density, P= pressure and γ is γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.

4. What is the mach number of an aircraft flying in air at a pressure of 101306N/m2 and velocity 556m/s?
a) 1.634
b) 2.145
c) 0.125
d) 1.225

Explanation: The answer is 1.634. Given P=101306N/m2, V=556m/s. We know that ρ and γ of air are ρ=1.225kg/m3 and 1.4. From the equation M=V$$\sqrt{\frac{\rho}{\gamma P}}$$
On substituting and solving,
M=556$$\sqrt{\frac{1.225}{1.4*101306}}$$
M=1.634.

5. What is the relation between mach number and pressure ratio?
a) $$\frac{p1}{p2}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}$$
b) $$\frac{p2}{p1}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}$$
c) $$\frac{p1}{p2}=\Big\{1+\frac{\gamma+1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}$$
d) $$\frac{p1}{p2}=\Big\{1-\frac{\gamma+1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}$$

Explanation: The relation between mach number and pressure is $$\frac{p1}{p2}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}$$ where p1, p2 are pressures at two points, M=mach number and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.

6. What is the mach number of aircraft flying in air where the pressure ratio is 1.893?
a) 2
b) 1
c) 3
d) 4

Explanation: The answer is 1. Given σ=1.893 and we know that γ for air is 1.4.
On substituting the values in the equation $$\frac{p_1}{p_2}=\Big\{1+\frac{\gamma-1}{2}(M)^2\Big\}^\frac{\gamma}{\gamma-1}$$
We get 1.893=$$\Big\{1+\frac{1.4-1}{2}(M)^2\Big\}^\frac{1.4}{1.4-1}$$
On solving we get M=1.

7. Mach number of an aircraft is affected by the shock waves created at the vortex of the aircraft.
a) True
b) False

Explanation: Mach number of an aircraft is affected by the shock waves created at the vortex of the aircraft. There are three types of shock waves they are normal shock waves, oblique shock waves and expanded waves.

8. What is the relationship between temperature and mach number?
a) T0=T$$\Big[1+\frac{\gamma-1}{2}M^2\Big]$$
b) T0=T$$\Big[1+\frac{\gamma+1}{2}M^2\Big]$$
c) T0=T$$\Big[1-\frac{\gamma-1}{2}M^2\Big]$$
d) T0=T$$\Big[1-\frac{\gamma+1}{2}M^2\Big]$$

Explanation: The relationship between temperature and mach number is T0=T$$\Big[1+\frac{\gamma-1}{2}M^2\Big]$$ where T is the temperature at that altitude, T_0 is the stagnation temperature, M is mach number and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.

9. Scale height is the description of how the altitude changes in the atmosphere.
a) True
b) False

Explanation: Scale height is the description of how the altitude changes in the atmosphere. It is the vertical distance measurement where the density and pressure decrease by the factor of $$\frac{1}{e}$$.

10. What will be the temperature of aircraft flying in air where the stagnation temperature is 288.15K and mach number is 1?
a) 250.15K
b) 240.125K
c) 300K
d) 270.18K

Explanation: The answer is 240.125K. Given T0=288.15K and M=1. By substituting the values in the formula T0=T$$\Big[1+\frac{\gamma-1}{2}M^2\Big]$$
On substituting 288.15=T[1+$$\frac{1.4-1}{2}1^2]$$
T=$$\frac{288.15}{1.2}$$
T=240.125K.

Sanfoundry Global Education & Learning Series – Aircraft Performance.

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