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A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in which the Mach number is 0.1. At a point on the airfoil, the pressure coefficient is measured to be -1.2. If the flow velocity is increased such that the free-stream Mach number is 0.6, the pressure coefficient at the same point on the airfoil will approximately be:
- a)-3.5
- b)-2.9
- c)-1.5
- d)-0.75
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in wh...
Explanation:
The pressure coefficient is defined as:
Cp = (P - P_inf) / (1/2 * rho * V_inf^2)
where P is the local pressure, P_inf is the free-stream pressure, rho is the air density, and V_inf is the free-stream velocity.
Given:
Mach number in the low-speed wind tunnel, M_1 = 0.1
Pressure coefficient at a point on the airfoil, Cp_1 = -1.2
At Mach number 0.1:
From the isentropic relations, we know that:
P_1 / P_inf = (1 + (gamma-1)/2 * M_1^2)^(gamma/(gamma-1))
where gamma is the ratio of specific heats.
For air, gamma = 1.4
Therefore, P_1 / P_inf = 0.990
Cp_1 = -1.2
At Mach number 0.6:
Using the same relations, we can find the pressure coefficient at Mach number 0.6:
P_2 / P_inf = (1 + (gamma-1)/2 * M_2^2)^(gamma/(gamma-1))
where M_2 = 0.6 is the new Mach number.
Therefore, P_2 / P_inf = 1.244
Using the definition of Cp:
Cp_2 = (P_2 - P_inf) / (1/2 * rho * V_inf^2)
Cp_2 = (1.244 * P_inf - P_inf) / (1/2 * rho * V_inf^2)
Cp_2 = 0.488 * Cp_1
Cp_2 = 0.488 * (-1.2)
Cp_2 = -0.586
Approximately, Cp_2 = -1.5 (option C is correct)
Note:
The change in Mach number causes changes in the flow properties, including pressure, density, and temperature. The pressure coefficient is a dimensionless quantity that relates the local pressure to the free-stream pressure and velocity. A negative value of Cp indicates that the local pressure is lower than the free-stream pressure.
The pressure coefficient is defined as:
Cp = (P - P_inf) / (1/2 * rho * V_inf^2)
where P is the local pressure, P_inf is the free-stream pressure, rho is the air density, and V_inf is the free-stream velocity.
Given:
Mach number in the low-speed wind tunnel, M_1 = 0.1
Pressure coefficient at a point on the airfoil, Cp_1 = -1.2
At Mach number 0.1:
From the isentropic relations, we know that:
P_1 / P_inf = (1 + (gamma-1)/2 * M_1^2)^(gamma/(gamma-1))
where gamma is the ratio of specific heats.
For air, gamma = 1.4
Therefore, P_1 / P_inf = 0.990
Cp_1 = -1.2
At Mach number 0.6:
Using the same relations, we can find the pressure coefficient at Mach number 0.6:
P_2 / P_inf = (1 + (gamma-1)/2 * M_2^2)^(gamma/(gamma-1))
where M_2 = 0.6 is the new Mach number.
Therefore, P_2 / P_inf = 1.244
Using the definition of Cp:
Cp_2 = (P_2 - P_inf) / (1/2 * rho * V_inf^2)
Cp_2 = (1.244 * P_inf - P_inf) / (1/2 * rho * V_inf^2)
Cp_2 = 0.488 * Cp_1
Cp_2 = 0.488 * (-1.2)
Cp_2 = -0.586
Approximately, Cp_2 = -1.5 (option C is correct)
Note:
The change in Mach number causes changes in the flow properties, including pressure, density, and temperature. The pressure coefficient is a dimensionless quantity that relates the local pressure to the free-stream pressure and velocity. A negative value of Cp indicates that the local pressure is lower than the free-stream pressure.
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A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in which the Mach number is 0.1. At a point on the airfoil, the pressure coefficient is measured to be -1.2. If the flow velocity is increased such that the free-stream Mach number is 0.6, the pressure coefficient at the same point on the airfoil will approximately be:a)-3.5b)-2.9c)-1.5d)-0.75Correct answer is option 'C'. Can you explain this answer?
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A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in which the Mach number is 0.1. At a point on the airfoil, the pressure coefficient is measured to be -1.2. If the flow velocity is increased such that the free-stream Mach number is 0.6, the pressure coefficient at the same point on the airfoil will approximately be:a)-3.5b)-2.9c)-1.5d)-0.75Correct answer is option 'C'. 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 A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in which the Mach number is 0.1. At a point on the airfoil, the pressure coefficient is measured to be -1.2. If the flow velocity is increased such that the free-stream Mach number is 0.6, the pressure coefficient at the same point on the airfoil will approximately be:a)-3.5b)-2.9c)-1.5d)-0.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in which the Mach number is 0.1. At a point on the airfoil, the pressure coefficient is measured to be -1.2. If the flow velocity is increased such that the free-stream Mach number is 0.6, the pressure coefficient at the same point on the airfoil will approximately be:a)-3.5b)-2.9c)-1.5d)-0.75Correct answer is option 'C'. Can you explain this answer?.
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