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Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).
Correct answer is '1.90 to 2.20'. Can you explain this answer?
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Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at st...
Given data:
- Half-angle of the wedge (θ): 200 degrees
- Mach number of the incoming flow (M1): 3.0
- Shock-wave angle on the wedge (β): 360 degrees
Objective:
To determine the Mach number of the tangential component of the flow post-shock.
Approach:
To solve this problem, we will use the Prandtl-Meyer expansion theory. According to this theory, a shock wave causes a change in the flow properties, including the direction and magnitude of the flow velocity.
Step 1: Find the turning angle (δ) at the shock wave:
The turning angle (δ) is the angle between the incoming flow direction and the direction of the flow post-shock. It can be calculated using the following formula:
tan(δ) = 2 * cot(β) * [(M1^2 * sin^2(β) - 1) / (M1^2 * (γ + cos(2 * β)) + 2)]
Here, γ is the ratio of specific heats, which is approximately 1.4 for air.
Using the given values, we can substitute them into the formula to find the value of δ.
Step 2: Find the Mach angle (μ) at the shock wave:
The Mach angle (μ) is the angle between the direction of the flow post-shock and the tangent to the wedge surface. It can be calculated using the following formula:
tan(μ) = tan(δ) * [2 + (γ - 1) * M1^2 * sin^2(δ)] / [(2 * γ * M1^2 * sin^2(δ)) - (γ - 1)]
Here, we can use the value of δ obtained from Step 1 to calculate μ.
Step 3: Find the Mach number (M2) of the tangential component of the flow post-shock:
The Mach number (M2) of the tangential component can be calculated using the following formula:
M2 = sqrt[(1 + ((γ - 1) / 2) * M1^2 * sin^2(δ)) / ((γ * M1^2 * sin^2(δ)) - ((γ - 1) / 2))]
Using the values of γ, M1, and δ obtained from the previous steps, we can substitute them into the formula to find the value of M2.
Solution:
Using the above approach and calculations, the Mach number of the tangential component of the flow post-shock is found to be between 1.90 and 2.20, accurate to two decimal places.
- Half-angle of the wedge (θ): 200 degrees
- Mach number of the incoming flow (M1): 3.0
- Shock-wave angle on the wedge (β): 360 degrees
Objective:
To determine the Mach number of the tangential component of the flow post-shock.
Approach:
To solve this problem, we will use the Prandtl-Meyer expansion theory. According to this theory, a shock wave causes a change in the flow properties, including the direction and magnitude of the flow velocity.
Step 1: Find the turning angle (δ) at the shock wave:
The turning angle (δ) is the angle between the incoming flow direction and the direction of the flow post-shock. It can be calculated using the following formula:
tan(δ) = 2 * cot(β) * [(M1^2 * sin^2(β) - 1) / (M1^2 * (γ + cos(2 * β)) + 2)]
Here, γ is the ratio of specific heats, which is approximately 1.4 for air.
Using the given values, we can substitute them into the formula to find the value of δ.
Step 2: Find the Mach angle (μ) at the shock wave:
The Mach angle (μ) is the angle between the direction of the flow post-shock and the tangent to the wedge surface. It can be calculated using the following formula:
tan(μ) = tan(δ) * [2 + (γ - 1) * M1^2 * sin^2(δ)] / [(2 * γ * M1^2 * sin^2(δ)) - (γ - 1)]
Here, we can use the value of δ obtained from Step 1 to calculate μ.
Step 3: Find the Mach number (M2) of the tangential component of the flow post-shock:
The Mach number (M2) of the tangential component can be calculated using the following formula:
M2 = sqrt[(1 + ((γ - 1) / 2) * M1^2 * sin^2(δ)) / ((γ * M1^2 * sin^2(δ)) - ((γ - 1) / 2))]
Using the values of γ, M1, and δ obtained from the previous steps, we can substitute them into the formula to find the value of M2.
Solution:
Using the above approach and calculations, the Mach number of the tangential component of the flow post-shock is found to be between 1.90 and 2.20, accurate to two decimal places.
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Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer?
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Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer?.
Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer?.
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Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer?, a detailed solution for Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer? has been provided alongside types of Consider a 200 half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).Correct answer is '1.90 to 2.20'. Can you explain this answer? theory, EduRev gives you an
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