1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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 \(\frac{1}{e}\).
8. 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.
9. The ratio of indicated temperature rise to ideal pressure rise is known as recovery factor.
a) True
b) False
Explanation: The ratio of indicated temperature rise to ideal pressure rise is known as recovery factor. It is given by the expression r=\(\frac{T_i-T}{T_t-T}\) where r is known as recovery factor, Ti is known as indicated total temperature, Tt is known as total temperature and T is known as static temperature.
10. Which of the following is the correct expression for recovery factor?
a) r=\(\frac{T_i+T}{T_t+T}\)
b) r=\(\frac{T_i-T}{T_t-T}\)
c) r=\(\frac{T_i+T}{T_t-T}\)
d) r=\(\frac{T-T_i}{T+T_t}\)
Explanation: The expression for recovery factor is given by r=\(\frac{T_i-T}{T_t-T}\) where r is known as recovery factor, Ti is known as indicated total temperature, Tt is known as total temperature and T is known as static temperature. The ratio of indicated temperature rise to ideal pressure rise is known as recovery factor.