HYPERSONIC AERODYNAMICS: MATHEMATICAL PROBLEMS MCQ
QUESTIONS AND DETAILED ANSWERS
1. Calculate the Mach number for an aircraft traveling at 1800 m/s at an altitude where the speed of
sound is 300 m/s.
Answer: Mach 6
2. If the dynamic pressure at Mach 6 is 150 kPa, what is the freestream static pressure assuming γ =
1.4?
Answer: 3.57 kPa
3. A hypersonic vehicle experiences a temperature of 1500 K at its stagnation point. If the freestream
temperature is 250 K, what is the Mach number? (Assume γ = 1.4)
Answer: Mach 5.77
4. Calculate the thickness of the shock layer for a blunt body with a radius of 1 m traveling at Mach 7.
(Assume δ/R ≈ 0.18/M∞)
Answer: 0.0257 m
5. What is the pressure ratio across a normal shock at Mach 8, assuming γ = 1.4?
Answer: 75.33
6. A hypersonic vehicle travels at Mach 10 at an altitude of 30 km. If the atmospheric density at this
altitude is 0.018 kg/m³, what is the dynamic pressure?
Answer: 81 kPa
7. Calculate the temperature behind a normal shock for a flow at Mach 6, given a freestream
temperature of 220 K and γ = 1.4.
Answer: 1848.8 K
8. What is the Knudsen number for a vehicle with a characteristic length of 5 m flying at an altitude
where the mean free path of air molecules is 0.1 mm?
Answer: 2 × 10⁻⁵
9. If the stagnation point heat flux on a hypersonic vehicle is 5 MW/m², what is the approximate nose
radius, assuming a velocity of 6 km/s and atmospheric density of 0.001 kg/m³?
Answer: 0.072 m
10. Calculate the Reynolds number for a hypersonic aircraft with a characteristic length of 20 m,
flying at Mach 7 at an altitude where the density is 0.01 kg/m³ and the dynamic viscosity is 1.5 × 10⁻⁵
Pa·s.
Answer: 9.33 × 10⁶
11. What is the speed of a hypersonic projectile traveling at Mach 15 in an atmosphere where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 4242.6 m/s
12. Calculate the thickness of the boundary layer at a distance of 2 m from the leading edge of a flat
plate in hypersonic flow at Mach 6, given a Reynolds number of 10⁷.
Answer: 0.0126 m
13. What is the Mach angle for a flow at Mach 8?
Answer: 7.18°
14. If the shock standoff distance for a sphere in hypersonic flow is 0.01 m, what is the approximate
Mach number? (Assume δ/R ≈ 0.18/M∞ and R = 0.5 m)
Answer: Mach 9
15. Calculate the temperature ratio across an oblique shock with a deflection angle of 15° in a Mach
10 flow. (Assume γ = 1.4)
Answer: 3.76
16. What is the maximum turn angle for an attached oblique shock at Mach 8? (Assume γ = 1.4)
Answer: 45.6°
17. Calculate the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at
Mach 12. (Assume γ = 1.4)
Answer: 1.829
18. If the shock wave angle is 12° in a hypersonic flow, what is the Mach number? (Use θ-β-M
relation)
Answer: Approximately Mach 9.5
19. What is the density ratio across a normal shock at Mach 15, assuming γ = 1.4?
Answer: 5.8
20. Calculate the Stanton number for a hypersonic flat plate with a heat flux of 2 MW/m², freestream
velocity of 5 km/s, density of 0.01 kg/m³, and temperature difference of 1000 K.
Answer: 0.008
21. What is the speed of sound in air at a temperature of 1500 K? (Assume γ = 1.4 and R = 287
J/(kg·K))
Answer: 775.2 m/s
22. Calculate the total temperature for a hypersonic flow at Mach 8, given a static temperature of
250 K. (Assume γ = 1.4)
Answer: 3650 K
23. What is the Prandtl-Meyer angle for a flow expanding from Mach 5 to Mach 8? (Assume γ = 1.4)
Answer: 25.1°
24. Calculate the shock detachment distance for a sphere with a radius of 0.1 m traveling at Mach 10.
(Use δ/R ≈ 0.18/M∞)
Answer: 0.0018 m
25. What is the ratio of specific heats (γ) for dissociated air at 3000 K?
Answer: Approximately 1.3
26. Calculate the Mach number behind a normal shock for a freestream Mach number of 12.
(Assume γ = 1.4)
Answer: 0.4754
27. What is the temperature in Kelvin of a hypersonic flow with a velocity of 6 km/s and a Mach
number of 20?
Answer: 450 K
28. Calculate the Newtonian pressure coefficient for a surface inclined at 30° to a Mach 10 flow.
Answer: 1.5
29. What is the entropy change across a normal shock at Mach 7? (Assume γ = 1.4 and R = 287
J/(kg·K))
Answer: 1149.3 J/(kg·K)
30. Calculate the thickness of the viscous shock layer for a flat plate at Mach 15, given a Reynolds
number of 10⁶ and a distance of 1 m from the leading edge.
Answer: 0.0158 m
31. What is the speed of a hypersonic aircraft traveling at Mach 8 at an altitude where the
temperature is 220 K? (Assume γ = 1.4)
Answer: 2376.8 m/s
32. Calculate the dynamic pressure for a vehicle traveling at Mach 6 at an altitude where the static
pressure is 1 kPa and γ = 1.4.
Answer: 25.2 kPa
33. What is the temperature ratio across a Prandtl-Meyer expansion from Mach 5 to Mach 8?
(Assume γ = 1.4)
Answer: 0.5625
34. Calculate the Mach number for a flow with a total temperature of 3000 K and a static
temperature of 500 K. (Assume γ = 1.4)
Answer: Mach 5.48
35. What is the Reynolds number for a hypersonic vehicle with a characteristic length of 10 m,
traveling at 6 km/s in an atmosphere with density 0.01 kg/m³ and viscosity 1.5 × 10⁻⁵ Pa·s?
Answer: 4 × 10⁶
36. Calculate the shock wave angle for an oblique shock with a deflection angle of 20° at Mach 10.
(Use θ-β-M relation)
Answer: Approximately 22.5°
37. What is the ratio of the boundary layer thickness to the shock layer thickness for a flat plate at
Mach 10? (Assume laminar flow)
Answer: Approximately 0.32
38. Calculate the Knudsen number for a vehicle with a characteristic length of 2 m flying at an
altitude where the mean free path of air molecules is 0.05 mm.
Answer: 2.5 × 10⁻⁵
39. What is the speed of a hypersonic missile traveling at Mach 12 in an atmosphere where the
temperature is 180 K? (Assume γ = 1.4)
Answer: 3230.4 m/s
40. Calculate the temperature behind an oblique shock with a deflection angle of 25° in a Mach 8
flow. (Assume γ = 1.4 and T₁ = 250 K)
Answer: 1837.5 K
41. What is the Mach number behind a Prandtl-Meyer expansion from Mach 6 to a pressure ratio of
0.1? (Assume γ = 1.4)
Answer: Approximately Mach 11.5
42. Calculate the stagnation pressure for a hypersonic flow at Mach 15, given a freestream static
pressure of 10 Pa. (Assume γ = 1.4)
Answer: 675.8 kPa
43. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.5 m at Mach
10? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.015 m
44. Calculate the Mach number for a hypersonic flow with a total temperature of 5000 K and a static
temperature of 300 K. (Assume γ = 1.4)
Answer: Mach 9.13
45. What is the pressure ratio across an oblique shock with a deflection angle of 30° at Mach 12?
(Use oblique shock relations)
Answer: Approximately 87.5
46. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1000 K and a freestream temperature of 250 K. (Assume viscosity ∝ T^0.7)
Answer: 0.3715
47. What is the Mach number at which the normal shock density ratio reaches 97% of its hypersonic
limit? (Assume γ = 1.4)
Answer: Approximately Mach 8.5
48. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.1 m traveling at
Mach 10 in an atmosphere with density 0.01 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 5.6 MW/m²
49. What is the Reynolds number behind a normal shock for a flow at Mach 12, given a freestream
Reynolds number of 10⁶? (Assume γ = 1.4)
Answer: Approximately 6.8 × 10⁷
50. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 100 kPa and a static
pressure of 1 kPa. (Assume γ = 1.4)
Answer: Mach 7.75
51. What is the shock standoff distance for a cylinder with a radius of 0.2 m traveling at Mach 15?
(Use δ/R ≈ 0.18/M∞)
Answer: 0.0024 m
52. Calculate the temperature in the shock layer of a hypersonic vehicle traveling at Mach 20, given a
freestream temperature of 220 K. (Assume perfect gas)
Answer: 9680 K
53. What is the Mach number behind an oblique shock with a shock angle of 15° in a Mach 10 flow?
(Use oblique shock relations)
Answer: Approximately Mach 8.2
54. Calculate the Stanton number for a flat plate in hypersonic flow with a Reynolds number of 10⁷
and a Prandtl number of 0.7. (Use St = 0.332Pr^(-2/3)Re^(-1/2))
Answer: 0.00166
55. What is the ratio of the viscous force to the pressure force on a flat plate at Mach 8? (Assume
laminar flow)
Answer: Approximately 0.125
56. Calculate the Mach number for a hypersonic flow with a total pressure of 1 MPa and a static
pressure of 100 Pa. (Assume γ = 1.4)
Answer: Mach 14.1
57. What is the temperature ratio across a Prandtl-Meyer expansion from Mach 7 to Mach 12?
(Assume γ = 1.4)
Answer: 0.5093
58. Calculate the shock detachment distance for a sphere with a radius of 0.5 m traveling at Mach 8.
(Use δ/R ≈ 0.18/M∞)
Answer: 0.01125 m
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
59. What is the Mach number at which the oblique shock angle becomes independent of the
freestream Mach number? (Assume γ = 1.4)
Answer: Approximately Mach 3
60. Calculate the Knudsen number for a vehicle with a characteristic length of 1 m flying at an
altitude where the mean free path of air molecules is 0.2 mm.
Answer: 2 × 10⁻⁴
61. What is the speed of a hypersonic aircraft traveling at Mach 18 at an altitude where the
temperature is 200 K? (Assume γ = 1.4)
Answer: 5091.2 m/s
62. Calculate the temperature behind a normal shock for a flow at Mach 15, given a freestream
temperature of 200 K and γ = 1.4.
Answer: 6930 K
63. What is the pressure coefficient at the stagnation point of a hypersonic vehicle traveling at Mach
20? (Assume γ = 1.4)
Answer: 1.846
64. Calculate the Mach number for a hypersonic flow with a total temperature of 8000 K and a static
temperature of 400 K. (Assume γ = 1.4)
Answer: Mach 10.2
65. What is the ratio of the viscous shock layer thickness to the inviscid shock layer thickness for a
flat plate at Mach 12? (Assume laminar flow)
Answer: Approximately 3.46
66. Calculate the Reynolds number behind an oblique shock with a deflection angle of 20° for a Mach
10 flow with a freestream Reynolds number of 10⁶. (Assume γ = 1.4)
Answer: Approximately 1.8 × 10⁷
67. What is the Mach number behind a Prandtl-Meyer expansion from Mach 8 to a pressure ratio of
0.05? (Assume γ = 1.4)
Answer: Approximately Mach 15.8
68. Calculate the stagnation point heat transfer rate for a sphere with a radius of 0.2 m traveling at
Mach 15 in an atmosphere with density 0.005 kg/m³. (Use Fay-Riddell correlation)
Answer: Approximately 8.2 MW/m²
69. What is the thickness of the entropy layer for a blunt body with a nose radius of 0.3 m at Mach
12? (Assume δₑ/R ≈ 0.3/M∞)
Answer: 0.0075 m
70. Calculate the Mach number for a hypersonic flow with a dynamic pressure of 200 kPa and a static
pressure of 500 Pa. (Assume γ = 1.4)
Answer: Mach 12.3
71. What is the shock wave angle for an oblique shock with a deflection angle of 10° at Mach 15?
(Use θ-β-M relation)
Answer: Approximately 11.5°
72. Calculate the temperature ratio across an oblique shock with a shock angle of 20° in a Mach 12
flow. (Assume γ = 1.4)
Answer: 4.89
73. What is the Mach number at which the normal shock temperature ratio reaches 95% of its
hypersonic limit? (Assume γ = 1.4)
Answer: Approximately Mach 7
74. Calculate the Chapman-Rubesin parameter for a hypersonic boundary layer with a wall
temperature of 1500 K and a freestream temperature of 200 K. (Assume viscosity ∝ T^0.7)
Answer: 0.2516
75. What is the ratio of
