Gas Dynamics Questions and Answers – Oblique Shock and Expansion Waves

This set of Gas Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Oblique Shock and Expansion Waves”.

1. What happens to the flow properties across an oblique shock?
a) Across an oblique shock, Mach number decreases whereas pressure and temperature increases
b) Across an oblique shock, Mach number increases whereas density and pressure decrease
c) Across an oblique shock, pressure and temperature decreases
d) Across an oblique shock, Mach number and total pressure increases

Explanation: Across an oblique shock, due to its non-isentropic nature, Mach number decreases, pressure, density, and temperature increases. Total pressure across the shock wave decreases.

2. What happens to the flow properties across an expansion fan?
a) Across an oblique shock, Mach number decreases whereas pressure and temperature increases
b) Across an oblique shock, Mach number increases whereas pressure and density decreases
c) Across an oblique shock, pressure and temperature increases
d) Across an oblique shock, Mach number and total pressure decreases

Explanation: Across an expansion fan, Mach number increases, pressure, density, and temperature decreases. Since the process is isentropic, stagnation properties like total pressure and temperature remain constant.

3. What are angles of the first and last Mach lines of an expansion fan?
a) μ1 = sin-1⁡$$\frac {1}{M_1}$$ and μ2 = sin-1⁡$$\frac {1}{M_2}$$
b) μ1 = sin-1⁡$$\frac {2}{M_1+M_2}$$ and μ2 = sin-1⁡$$\frac {1}{M_2}$$
c) μ1 = sin-1⁡$$\frac {2}{M_1+M_2}$$ and μ2 = sin-1⁡$$\frac {2}{M_1+M_2}$$
d) μ1 = sin-1⁡$$\frac {1}{M_1}$$ and μ1 = sin-1$$\frac {2}{M_1+M_2}$$

Explanation: Since each wave in the expansion fan turns the flow in small steps, the first Mach line relates to the Mach number upstream of the flow and the last Mach line relates to the Mach number of the downstream flow across the expansion fan. Hence, μ1 = sin-1⁡$$\frac {1}{M_1}$$ and μ2 = sin-1⁡$$\frac {1}{M_2}$$.

4. What is the Mach number of the flow after the shock and normal to the oblique shock? Mach number downstream of the flow is, M2 = 1.1, shock angle, β = 60°, and wall deflection angle, θ = 4.018°.
a) 0.77
b) 1.270
c) 0.952
d) 0.912

Explanation: The Mach number of the flow after the shock and normal to the oblique shock is given by, My = M2sin⁡(β – θ) = 1.1 × sin⁡(60 – 4.018) = 0.912.

5. What is true about a supersonic flow around a wedge?
a) The flow changes its direction smoothly and pressure decreases with acceleration
b) There is a sudden change in flow direction at the body and pressure increases downstream of the shock
c) The flow changes its direction abruptly and pressure decreases with acceleration
d) The flow changes its direction smoothly and pressure increases downstream with acceleration

Explanation: When the flow is supersonic around a wedge, it is observed that there is a sudden change in flow direction at the body due to the formation of a shock wave which is an isentropic process. In an isentropic process, the static properties (pressure, temperature, density) increase almost instantly.

6. What are the wave angles (β) possible for a given Mach number (M1)?
a) 0 < β ≤ 90°
b) sin-1⁡$$\frac {1}{M_1}$$ ≤ β ≤ 90°
c) 0 < β ≤ sin-1⁡⁡$$\frac {1}{M_1}$$
d) 0 < β ≤ 180°

Explanation: Since the normal component of the velocity ahead of the shock is supersonic, we can show that M1 sin⁡(β) ≥ 1, which gives us the minimum value of the shock angle. The maximum wave angle is that of a normal shock which is 90°.

7. The ratio of the densities of the flow downstream and upstream of the oblique shock is 1.5157. If the normal component of the velocity of the upstream flow is 445.9 m/s, then what is the normal component of the velocity downstream of the shock?
a) 294.18 m/s
b) 269.6 m/s
c) 306 m/s
d) 255 m/s

Explanation: According to the continuity equation, ρ1A1Vx1 = ρ2A1Vx2, since the area upstream and downstream of the shock doesn’t change, we can show that, ⁡$$\frac {V_{x1}}{V_{x2}} = \frac {\rho_2}{\rho_1}$$. Putting the given values, we get Vx2 = $$\frac {445.9}{1,5157}$$ = 294.18 m/s.

8. Which of the following is true regarding the θ-β-M relation?
a) There is a maximum value of deflection angle for a given Mach number for a straight oblique wave
b) There are two possible solutions for any given deflection angle and Mach number
c) The θ-β-M relation has a solution only when the Mach number of the flow downstream is less than unity
d) There are two values of deflection angle for a given Mach number and shock angle

Explanation: The minimum value of the deflection angle is 0 and the maximum value is attained at M1 = ∞. There are two possible solutions (shock angles), within the limiting values of the deflection angle and Mach number.

9. Choose the correct statement.
a) Strong shock solution is smaller in value than the weak shock solution
b) For a strong shock solution, the flow downstream of the shock is supersonic
c) A weak shock solution is most common among experimental results
d) For a weak shock solution, the flow downstream of the shock is subsonic

Explanation: From the two solutions obtained from the θ-β-M relation, smaller value corresponds to a weak shock solution and the larger value corresponds to a strong shock solution. Flow behind the shock in strong shock and weak shock solutions are subsonic and supersonic respectively. Experimentally, weak shock solutions are always seen.

10. What are the values of shock angles (β), when the deflection (θ) is zero, for a given Mach number?
a) β = 0, 90°
b) β = μ, 60°
c) β = 0, 60°
d) β = μ, 90°

Explanation: When the deflection is zero, the θ-β-M equation reduces to (M1sin⁡β)2⁡ = 1. Two solutions obtained for shock angles from the above relation are, β = -90°, 90°. When the shock angle is 90°, a normal shock is observed. But -90° is not possible and hence it takes some limiting value, μ.

11. What is the θ-β-M equation reduced to when flow Mach number is very large and for very small deflection angles?
a) β = $$\frac {γ+1}{2}$$ θ
b) β = $$\frac {γ+2}{1}$$ θ
c) θ = $$\frac {γ+1}{2}$$ β
d) θ = $$\frac {γ+2}{1}$$ β

Explanation: When M1 is very large and deflection angle is small, then shock angle, β << 1, but M1β >> 1. From this assumption, we can reduce the θ-β-M equation into, β = $$\frac {γ+1}{2}$$θ.

12. What is observed with 3-dimensional cone supersonic flow that is different from 2-dimensional flow?
a) The pressure is constant over the surface of the cone
b) Streamlines are straight and parallel to the conical surface behind the shock
c) Weaker shocks are observed in 3D than in 2D
d) Adiabatic nature of the wave is absent in 3-dimensional flow

Explanation: 3D provides extra space for the flow to move and hence relieving the flow from stress concentration. Hence weaker shocks are observed in 3D than in 2D. Streamlines are curved and pressure is not constant over the surface of the cone.

13. Which of the following best describes a shock polar?
a) Shock polar is the locus of all the velocities behind the shock for varying deflection angle from zero to the maximum deflection angle
b) Shock polar is the graphical representation of weak shocks properties
c) Shock polar is the locus of all the shock angles behind the shock for varying Mach number from one to infinity
d) Shock polar is the graphical representation of normal shock properties

Explanation: Shock polar is a graphical representation of oblique shock properties. It is the loci of all such points for deflection angle from zero to maximum deflection, representing all the velocities behind the shock.

14. Which is true regarding the dimensionless shock polar?
a) Characteristic Mach number is used to represent the velocity of the flow ahead and behind the shock
b) Higher Mach number represents stronger shock
c) Dimensionless shock polar is not very compact and hence is not used often
d) Inside the sonic circle in shock polar, all velocities are supersonic

Explanation: Characteristic Mach Number is used instead of only velocity or Mach number because when Mach number becomes infinity, characteristic Mach number becomes 2.45, which makes the graph more compact. All velocities inside the sonic circle are subsonic and outside it, are supersonic.

15. What is curve generated in shock polar for Mach number equal to infinity?
a) Circle
b) Ellipse
c) Parabola
d) Hyperbola

Explanation: When Mach number reaches infinity the shock polar is a circle. The circle lies between 0.41 to 2.45 characteristic Mach number values, which gives the diameter of the circle. This is the only circular curve other than the sonic circle in shock polar.

Sanfoundry Global Education & Learning Series – Gas Dynamics.

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