STUDY OF SUPERSONIC AND HYPERSONIC AIRCRAFT AND PROPULSION
SYSTEMS: 100 MULTIPLE CHOICE QUESTIONS
1. At what Mach number does an aircraft transition from supersonic to hypersonic flight?
a) Mach 3
b) Mach 4
c) Mach 5
d) Mach 6
Answer: c) Mach 5
2. The shock wave angle β for a wedge-shaped airfoil with half-angle θ in supersonic flow is given by
the θ-β-M relation. Which of the following is correct?
a) sin β = sin θ / M
b) tan β = 2 cot θ [(M² sin² β - 1) / (M² (γ + cos 2β) + 2)]
c) cos β = (M² - 1) / (M² + 1)
d) tan β = 2 (M² sin² β - 1) / [M² (γ + cos 2β) + 2]
Answer: b) tan β = 2 cot θ [(M² sin² β - 1) / (M² (γ + cos 2β) + 2)]
3. The Prandtl-Meyer function ν(M) for a supersonic Mach number M is given by:
a) ν(M) = √((γ+1)/(γ-1)) tan⁻¹[√((γ-1)/(γ+1)(M²-1))] - tan⁻¹√(M²-1)
b) ν(M) = √((γ+1)/(γ-1)) tan⁻¹[√((γ-1)/(γ+1)(M²-1))] + tan⁻¹√(M²-1)
c) ν(M) = √((γ-1)/(γ+1)) tan⁻¹[√((γ+1)/(γ-1)(M²-1))] - tan⁻¹√(M²-1)
d) ν(M) = √((γ-1)/(γ+1)) tan⁻¹[√((γ+1)/(γ-1)(M²-1))] + tan⁻¹√(M²-1)
Answer: b) ν(M) = √((γ+1)/(γ-1)) tan⁻¹[√((γ-1)/(γ+1)(M²-1))] + tan⁻¹√(M²-1)
4. In a supersonic wind tunnel, the area ratio A/A* for a given Mach number M > 1 is given by:
a) (A/A*)² = [(γ+1)/2]^((γ+1)/(γ-1)) * [1 + ((γ-1)/2)M²]^((γ+1)/(γ-1)) / M²
b) (A/A*)² = [(γ+1)/2]^((γ+1)/(γ-1)) * [1 + ((γ-1)/2)M²]^((γ+1)/(γ-1)) * M²
c) (A/A*)² = [(γ-1)/2]^((γ+1)/(γ-1)) * [1 + ((γ+1)/2)M²]^((γ+1)/(γ-1)) / M²
d) (A/A*)² = [(γ-1)/2]^((γ+1)/(γ-1)) * [1 + ((γ+1)/2)M²]^((γ+1)/(γ-1)) * M²
Answer: a) (A/A*)² = [(γ+1)/2]^((γ+1)/(γ-1)) * [1 + ((γ-1)/2)M²]^((γ+1)/(γ-1)) / M²
5. The temperature ratio across a normal shock wave in a perfect gas is given by:
a) T₂/T₁ = [2γM₁² - (γ-1)] [(γ-1)M₁² + 2] / [(γ+1)²M₁²]
b) T₂/T₁ = [2γM₁² + (γ-1)] [(γ-1)M₁² + 2] / [(γ+1)²M₁²]
c) T₂/T₁ = [2γM₁² - (γ-1)] [(γ+1)M₁² + 2] / [(γ-1)²M₁²]
d) T₂/T₁ = [2γM₁² + (γ-1)] [(γ+1)M₁² + 2] / [(γ-1)²M₁²]
Answer: a) T₂/T₁ = [2γM₁² - (γ-1)] [(γ-1)M₁² + 2] / [(γ+1)²M₁²]
6. The pressure ratio across an oblique shock wave with upstream Mach number M₁ and shock angle
β is:
a) p₂/p₁ = 1 + (2γ/(γ+1)) (M₁² sin² β - 1)
b) p₂/p₁ = 1 + (2γ/(γ-1)) (M₁² sin² β - 1)
c) p₂/p₁ = 1 + (2γ/(γ+1)) (M₁² cos² β - 1)
d) p₂/p₁ = 1 + (2γ/(γ-1)) (M₁² cos² β - 1)
Answer: a) p₂/p₁ = 1 + (2γ/(γ+1)) (M₁² sin² β - 1)
7. The Rankine-Hugoniot equation for a normal shock wave relates the upstream and downstream
Mach numbers M₁ and M₂. Which of the following is correct?
a) M₁²M₂² = (γ-1)M₁² + 2 / (γ-1)M₂² + 2
b) M₁²/M₂² = (γ-1)M₁² + 2 / (γ-1)M₂² + 2
c) M₁²M₂² = (γ+1)M₁² + 2 / (γ+1)M₂² + 2
d) M₁²/M₂² = (γ+1)M₁² + 2 / (γ+1)M₂² + 2
Answer: b) M₁²/M₂² = (γ-1)M₁² + 2 / (γ-1)M₂² + 2
8. The ratio of specific heats γ for air at standard conditions is approximately:
a) 1.2
b) 1.3
c) 1.4
d) 1.5
Answer: c) 1.4
9. The speed of sound a in a perfect gas is given by:
a) a = √(γRT)
b) a = √(γP/ρ)
c) a = √(γPρ)
d) Both a and b
Answer: d) Both a and b
10. The stagnation temperature T₀ in terms of static temperature T and Mach number M is:
a) T₀/T = 1 + ((γ-1)/2)M²
b) T₀/T = 1 + ((γ+1)/2)M²
c) T₀/T = 1 + ((γ-1)/2)M
d) T₀/T = 1 + ((γ+1)/2)M
Answer: a) T₀/T = 1 + ((γ-1)/2)M²
11. The maximum turn angle θmax for an oblique shock occurs when the downstream Mach number
M₂ is:
a) M₂ = 1
b) M₂ = √((γ-1)/(γ+1))
c) M₂ = √((γ+1)/(γ-1))
d) M₂ = γ
Answer: a) M₂ = 1
12. In a Scramjet engine, the combustion process ideally takes place at:
a) Subsonic speeds
b) Sonic speed
c) Supersonic speeds
d) Hypersonic speeds
Answer: c) Supersonic speeds
13. The lift coefficient CL for a thin airfoil at small angle of attack α in supersonic flow is given by:
a) CL = 4α/√(M²-1)
b) CL = 2α/√(M²-1)
c) CL = 4α√(M²-1)
d) CL = 2α√(M²-1)
Answer: a) CL = 4α/√(M²-1)
14. The wave drag coefficient CD,w for a thin airfoil at small angle of attack α in supersonic flow is
given by:
a) CD,w = 4α²/√(M²-1)
b) CD,w = 2α²/√(M²-1)
c) CD,w = 4α²√(M²-1)
d) CD,w = 2α²√(M²-1)
Answer: a) CD,w = 4α²/√(M²-1)
15. The critical Mach number Mcr for a thin airfoil is the freestream Mach number at which local
sonic flow first appears. It is approximately given by:
a) Mcr ≈ 1 / √(1 + (γ+1)/2 * Cpmin)
b) Mcr ≈ 1 / √(1 - (γ-1)/2 * Cpmin)
c) Mcr ≈ √(1 + (γ+1)/2 * Cpmin)
d) Mcr ≈ √(1 - (γ-1)/2 * Cpmin)
Answer: b) Mcr ≈ 1 / √(1 - (γ-1)/2 * Cpmin)
16. The Busemann biplane is a supersonic airfoil configuration that theoretically produces:
a) Zero wave drag
b) Zero lift
c) Maximum lift-to-drag ratio
d) Maximum wave drag
Answer: a) Zero wave drag
17. The shock detachment distance δ for a blunt body in supersonic flow is proportional to:
a) δ ∝ R/M²
b) δ ∝ R/M
c) δ ∝ RM²
d) δ ∝ RM
Where R is the body radius of curvature and M is the freestream Mach number.
Answer: a) δ ∝ R/M²
18. The Ackeret theory for supersonic thin airfoils gives the pressure coefficient Cp as:
a) Cp = 2α/√(M²-1)
b) Cp = 4α/√(M²-1)
c) Cp = 2α√(M²-1)
d) Cp = 4α√(M²-1)
Where α is the angle of attack.
Answer: a) Cp = 2α/√(M²-1)
19. The Mach angle μ for a flow with Mach number M > 1 is given by:
a) sin μ = 1/M
b) cos μ = 1/M
c) tan μ = 1/M
d) cot μ = 1/M
Answer: a) sin μ = 1/M
20. The Kantrowitz limit for air intake starting in a supersonic flow is approximately:
a) M∞ ≈ 1.5
b) M∞ ≈ 2.0
c) M∞ ≈ 2.5
d) M∞ ≈ 3.0
Answer: b) M∞ ≈ 2.0
21. The Oswatitsch Mach number independence principle states that for M » 1:
a) CD ∝ 1/M
b) CD ∝ 1/M²
c) CD is independent of M
d) CD ∝ M
Where CD is the drag coefficient.
Answer: c) CD is independent of M
22. The hypersonic similarity parameter K is defined as:
a) K = M∞ * (t/c)
b) K = M∞² * (t/c)
c) K = M∞ / (t/c)
d) K = M∞² / (t/c)
Where t/c is the thickness-to-chord ratio.
Answer: b) K = M∞² * (t/c)
23. In hypersonic flow, the shock layer thickness δ scales with the body thickness t as:
a) δ/t ∝ 1/M∞
b) δ/t ∝ 1/M∞²
c) δ/t ∝ M∞
d) δ/t ∝ M∞²
Answer: a) δ/t ∝ 1/M∞
24. The Newtonian impact theory for hypersonic flow gives the pressure coefficient Cp as:
a) Cp = 2 sin² θ
b) Cp = 2 cos² θ
c) Cp = K sin² θ
d) Cp = K cos² θ
Where θ is the local body slope and K is a constant.
Answer: a) Cp = 2 sin² θ
25. The modified Newtonian theory for hypersonic flow gives the pressure coefficient Cp as:
a) Cp = Cp,max sin² θ
b) Cp = Cp,max cos² θ
c) Cp = 2 sin² θ
d) Cp = 2 cos² θ
Where Cp,max is the stagnation point pressure coefficient.
Answer: a) Cp = Cp,max sin² θ
26. The stagnation point heat transfer rate in hypersonic flow is proportional to:q
a) q ∝ V∞²
b) q ∝ V∞³
c) q ∝ √ρ∞
d) q ∝ ρ∞
Where V∞ is the freestream velocity and ρ∞ is the freestream density.
Answer: b) q ∝ V∞³
27. The Reynolds analogy relates the skin friction coefficient Cf to the Stanton number St by:
a) St = Cf/2
b) St = Cf
c) St = 2Cf
d) St = Cf/4
Answer: a) St = Cf/2
28. The temperature ratio across a normal shock wave in air (γ = 1.4) at M₁ = 5 is approximately:
a) T₂/T₁ ≈ 3.5
b) T₂/T₁ ≈ 4.5
c) T₂/T₁ ≈ 5.5
d) T₂/T₁ ≈ 6.5
Answer: c) T₂/T₁ ≈ 5.5
29. The pressure ratio across a normal shock wave in air (γ = 1.4) at M₁ = 5 is approximately:
a) p₂/p₁ ≈ 29
b) p₂/p₁ ≈ 39
c) p₂/p₁ ≈ 49
d) p₂/p₁ ≈ 59
Answer: a) p₂/p₁ ≈ 29
30. The Mach number behind a normal shock wave in air (γ = 1.4) at M₁ = 5 is approximately:
a) M₂ ≈ 0.3
b) M₂ ≈ 0.4
c) M₂ ≈ 0.5
d) M₂ ≈ 0.6
Answer: b) M₂ ≈ 0.4
31. The maximum deflection angle for an attached oblique shock in air (γ = 1.4) at M₁ = 3 is
approximately:
a) θmax ≈ 24°
b) θmax ≈ 28°
c) θmax ≈ 32°
d) θmax ≈ 36°
Answer: c) θmax ≈ 32°
32. The shock standoff distance δ for a sphere of radius R in a hypersonic flow (M » 1) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
33. The ratio of specific heats γ for a diatomic gas at high temperatures (where vibrational modes are
fully excited) is approximately:
a) γ ≈ 1.2
b) γ ≈ 1.3
c) γ ≈ 1.4
d) γ ≈ 1.5
Answer: a) γ ≈ 1.2
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
34. The Mach number at which the normal shock total pressure ratio (p₀₂/p₀₁) is 0.5 for air (γ = 1.4) is
approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
35. The area ratio A/A* for a Mach 3 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 2.0
b) A/A* ≈ 3.0
c) A/A* ≈ 4.0
d) A/A* ≈ 5.0
Answer: c) A/A* ≈ 4.0
36. The Prandtl-Meyer function ν(M) for M = 2 in air (γ = 1.4) is approximately:
a) ν(2) ≈ 20°
b) ν(2) ≈ 30°
c) ν(2) ≈ 40°
d) ν(2) ≈ 50°
Answer: b) ν(2) ≈ 30°
37. The ratio of dynamic pressure q₂ to q₁ across a normal shock wave at M₁ = 3 in air (γ = 1.4) is
approximately:
a) q₂/q₁ ≈ 0.2
b) q₂/q₁ ≈ 0.3
c) q₂/q₁ ≈ 0.4
d) q₂/q₁ ≈ 0.5
Answer: c) q₂/q₁ ≈ 0.4
38. The Taylor-Maccoll equation for conical flow is:
a) (1 - V²/a²)dV/dθ + (2/r)(1 - V²/a²)V = 0
b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
c) (1 - V²/a²)d²V/dθ² + (2/r)(1 - V²/a²)dV/dθ = 0
d) (V² - a²)d²V/dθ² + (2/r)(V² - a²)dV/dθ = 0
Answer: b) (V² - a²)dV/dθ + (2/r)(V² - a²)V = 0
39. The Rayleigh-Pitot formula relates the ratio of pitot pressure p₀₂ to static pressure p₁ for a
supersonic flow:
a) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
b) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
d) p₀₂/p₁ = [(γ+1)M₁²/(2+(γ-1)M₁²)]^(γ/(γ-1)) * [(1-γ+2γM₁²)/(γ+1)]
Answer: c) p₀₂/p₁ = [(γ+1)²M₁²/(4γM₁² - 2(γ-1))]^(γ/(γ-1)) * [(γ+1)/(2γM₁²-γ+1)]
40. The shock wave angle β for a wedge with half-angle θ = 15° at M₁ = 3 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: b) β ≈ 35°
41. The pressure coefficient Cp at the stagnation point of a body in hypersonic flow (M » 1) is
approximately:
a) Cp,max ≈ 1.8
b) Cp,max ≈ 1.9
c) Cp,max ≈ 2.0
d) Cp,max ≈ 2.1
Answer: a) Cp,max ≈ 1.8
42. The Mach number at which the maximum total pressure recovery for a normal shock is 50% in air
(γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
43. The Mach angle μ for a flow with Mach number M = 3 is:
a) μ ≈ 19.5°
b) μ ≈ 21.5°
c) μ ≈ 23.5°
d) μ ≈ 25.5°
Answer: a) μ ≈ 19.5°
44. The ratio of specific heats γ for a monatomic gas is:
a) γ = 4/3
b) γ = 5/3
c) γ = 6/5
d) γ = 7/5
Answer: b) γ = 5/3
45. The Mach number at which the ratio of static pressure to total pressure (p/p₀) is 0.1 for air (γ =
1.4) is approximately:
a) M ≈ 2.5
b) M ≈ 3.0
c) M ≈ 3.5
d) M ≈ 4.0
Answer: b) M ≈ 3.0
46. The shock detachment distance δ for a sphere of radius R at M = 3 in air (γ = 1.4) is
approximately:
a) δ/R ≈ 0.1
b) δ/R ≈ 0.2
c) δ/R ≈ 0.3
d) δ/R ≈ 0.4
Answer: b) δ/R ≈ 0.2
47. The maximum turn angle θmax for an attached oblique shock at M = 5 in air (γ = 1.4) is
approximately:
a) θmax ≈ 30°
b) θmax ≈ 35°
c) θmax ≈ 40°
d) θmax ≈ 45°
Answer: c) θmax ≈ 40°
48. The Mach number behind an oblique shock with upstream Mach number M₁ = 4 and shock angle
β = 30° in air (γ = 1.4) is approximately:
a) M₂ ≈ 2.5
b) M₂ ≈ 3.0
c) M₂ ≈ 3.5
d) M₂ ≈ 4.0
Answer: b) M₂ ≈ 3.0
49. The ratio of total temperature T₀₂ to T₀₁ across a normal shock wave is:
a) T₀₂/T₀₁ = 1
b) T₀₂/T₀₁ > 1
c) T₀₂/T₀₁ < 1
d) T₀₂/T₀₁ depends on the Mach number
Answer: a) T₀₂/T₀₁ = 1
50. The Mach number at which the ratio of dynamic pressure to total pressure (q/p₀) is maximum for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
51. The pressure ratio p₂/p₁ across an oblique shock wave with upstream Mach number M₁ = 3 and
shock angle β = 35° in air (γ = 1.4) is approximately:
a) p₂/p₁ ≈ 3.5
b) p₂/p₁ ≈ 4.5
c) p₂/p₁ ≈ 5.5
d) p₂/p₁ ≈ 6.5
Answer: c) p₂/p₁ ≈ 5.5
52. The Mach number at which the ratio of static temperature to total temperature (T/T₀) is 0.5 for
air (γ = 1.4) is approximately:
a) M ≈ 1.5
b) M ≈ 2.0
c) M ≈ 2.5
d) M ≈ 3.0
Answer: b) M ≈ 2.0
53. The shock wave angle β for a wedge with half-angle θ = 20° at M₁ = 4 in air (γ = 1.4) is
approximately:
a) β ≈ 30°
b) β ≈ 35°
c) β ≈ 40°
d) β ≈ 45°
Answer: c) β ≈ 40°
54. The Prandtl-Meyer function ν(M) for M = 3 in air (γ = 1.4) is approximately:
a) ν(3) ≈ 40°
b) ν(3) ≈ 50°
c) ν(3) ≈ 60°
d) ν(3) ≈ 70°
Answer: b) ν(3) ≈ 50°
55. The area ratio A/A* for a Mach 4 flow in air (γ = 1.4) is approximately:
a) A/A* ≈ 5.0
b) A/A* ≈ 6.0
c) A/A* ≈ 7.0
d) A/A* ≈ 8.0
Answer: c) A/A* ≈ 7.0
56. The ratio of dynamic pressure q₂ to q₁ across an oblique shock wave with M₁ = 4 and β = 30° in air
(γ = 1.4) is approximately:
a) q₂/q₁ ≈ 0.6
b) q₂/q₁ ≈ 0.7
c) q₂/q₁ ≈ 0.8
d) q₂/q₁ ≈ 0.9
Answer: c) q₂/q₁ ≈ 0.8
57. The Mach number at which the ratio of static density to total density (ρ/ρ₀) is 0.25 for air (γ = 1.4)
is approximately:
a) M ≈ 2.0
b) M ≈ 2.5
c) M ≈ 3.0
d) M ≈ 3.5
Answer: b) M ≈ 2.5
58. The pressure coefficient Cp for a wedge with half-angle θ = 10° at M = 3 in air (γ = 1.4) is
approximately:
a) Cp ≈ 0.2
b) Cp ≈ 0.3
c) Cp ≈ 0.4
d) Cp ≈ 0.5
Answer: c) Cp ≈ 0.4
59. The ratio of total pressure p₀₂ to p₀₁ across an oblique shock wave with M₁ = 3 and β = 35° in air (γ
= 1.4) is approximately:
a) p₀₂/p₀₁ ≈ 0.7
b) p₀₂/p₀₁ ≈ 0.8
c) p₀₂/p₀₁ ≈ 0.9
d) p₀₂/p₀₁ ≈ 1.0
Answer: c) p₀₂/p₀₁ ≈ 0.9
60. The Mach number at which the ratio of static enthalpy to total enthalpy (h/h₀)
