Important

Question 1

Explain how the panel method uses elementary solutions to model flow over a wing.

Answer 1

• Elementary solutions to linear Laplace equation so we can use SUPERPOSITION.
• Discretise the wing with many elemental solutions
• Satisfy boundary conditions (flow through the surface)
• All elements contribute to induced velocity at all “location” points

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Question 2

What are the two theorems of Helmholtz’s?

Answer 2

1. strength of vortex filament is constant along its length
2. A vortex filament cannot end in a fluid; it must extend to boundaries of the fluid or form a closed path.

Question 3

What is the Biot-Savart Law?

Answer 3

Establishes the velocity induced in a point due to any vortex filament.

Question 4

What are the equations for Kutta-Joukowski Theorem and d’Alembert paradox

Answer 4

Lift per unit span is proportional to circulation.

Lift per unit span = densityvelocitycirculation

Drag per unit span = 0

Question 5

What is the Kutta condition?

Answer 5

States that the circulation around the aerofoil is just the right amount to ensure the flow leaves the trailing edge smoothly.

Question 6

What is Kelvins circulation Theorem?

Answer 6

The time rate of change of circulation around a closed curve remains constant.

This does not mean there is no change at all. It means that a change of circulation in time also requires a change in space

Question 7

What is Prandtl’s lifting line theory?

Answer 7

Instead of one vortex ring (or horseshoe), we have multiple to prevent downs at the tips becoming infinite.

Bound vertex giving lift through outta joukowski theorem.

Vortex strength goes to 0 at wing tip (not infinity)

Question 8

Whats the mathematical character of the blasiup boundary layer equation?

Answer 8

Single, third order, non-linear ODE