# Aerodynamics Questions and Answers – The Kutta-Joukowski Theorem

This set of Aerodynamics Multiple Choice Questions & Answers (MCQs) focuses on “The Kutta-Joukowski Theorem”.

1. Is Kutta-Joukowski theorem is fundamental theorem of aerodynamics?
a) True
b) False

Explanation: The Kutta-Joukowski theorem is a fundamental theorem of aerodynamics, this can be used for calculating of lift of an airfoil, or of any two-dimensional bodies including circular cylinders translating in a uniform fluid at a constant speed large enough so, that the flow seen in the body is fixed frame is steady and unseparated.

2. Is Kutta-Joukowski theorem relate to lift?
a) False
b) True

Explanation: The Kutta-Joukowski theorem relates the lift generated by an airfoil, to the speed of the airfoil. Through the fluid, the density of the fluid and the circulation. This theorem relates lift to circulation much like the Magnus effect relates to side force to the rotation.

3. Define circulation.
a) Line integral around a closed loop enclosing the airfoil
b) Line integral around an open loop enclosing the airfoil
c) Line integral around an in loop enclosing the airfoil
d) Line integral of airfoil

Explanation: Circulation is defined as the line integral around a closed loop enclosing the airfoil of the component of the velocity of the fluid tangent to the loop. To calculate the force on an airfoil, outside the boundary layer the vorticity is zero, everywhere the circulation is the same around every circuit.

4. Define Kutta-Joukowski theorem.
a) Lift per unit span on the airfoil
b) Drag per unit span on the airfoil
c) Moment per unit span on the airfoil
d) Thrust per unit span on the airfoil

Explanation: The Kutta-Joukowski theorem states that lift per unit span on a Two-Dimensional body, is directly propositional to the circulation around the body. It is a fundamental theorem of aerodynamics used for the calculation of the lift of an airfoil and any two-dimensional body.

5. What is the angle of attack of lift producing airfoil?
a) Angle of attack less than zero
b) Angle of attack greater than zero
c) Angle of attack is zero
d) Angle of attack remains the same

Explanation: A lift producing airfoil either has camber or is translating in a uniform fluid at an angle of attack greater than zero. Moreover, it must have a sharp trailing edge. An airfoil generates lift by exerting a downward force on the air as it flows past.
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6. How the fluid moves on the airfoil?
a) Lower surface
b) Upper and middle surface
c) Upper surface
d) Lower and upper surface

Explanation: Fluid moving along the lower and upper surface of the airfoil should meet at the sharp trailing edge. Since viscous dissipation prevents the fluid to turn around the sharp edge. This is known as the Kutta-Condition for real flow.

7. What is the condition for Kutta and Joukowski theorem?
a) Pressure and lift
b) Pressure and drag
c) Drag and lift
d) Lift and moment

Explanation: Kutta and Joukowski discovered that for computing, the pressure and lift of a thin enough airfoil for flow with large enough Reynolds number and at small enough angle of attach the flow can be assumed inviscid in the entire region provided the Kutta condition is imposed.

8. What is the flow outside the airfoil?
a) Irrotational
b) Rotational
c) Circumferential
d) Constant

Explanation: The flow outside the airfoil is irrotational and the circulation around any closed curve not enclosing airfoil is consequently zero. When the boundary layer separates, its displacement thickness increases sharply, which modifies the outside potential flow and pressure field.

9. How rotating flow is induced?
a) Joint effect of airfoil
b) Joint effect of chord
c) Joint effect of camber
d) Joint effect of camber line

Explanation: Rotating flow is induced by the joint effect of camber, angle of attack and sharp trailing edge of the airfoil and should not be confused with a vortex like a tornado encircling the cylinder or wing of an airplane in flight.

10. Kutta-Joukowski theorem refers to __________
a) two-dimensional flow around an airfoil
b) one-dimensional flow around an airfoil
c) three-dimensional flow around an airfoil
d) flows around an airfoil

Explanation: Kutta-Joukowski theorem refers to Two-Dimensional flow around an airfoil and determines the lift generated by one unit of a span. Kutta-Joukowski theorem is an inviscid theory, but it is a good approximation for real viscous flow in typical aerodynamic applications.

11. What is the condition for rotational flow in Kutta-Joukowski theorem?
a) Small number of unsteady flow
b) Large number of unsteady flow
c) Large number of steady flow
d) Small number of steady flow

Explanation: When there are free vortices outside of the body as may be the case for a large number of unsteady flow, the flow is rotational. A fluid is said to be rotational if fluid particles are rotating about their own mass center, otherwise, flow is irrotational.

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