Example sheet 1

Question 1

Wind tunnel model is taking place. Scale factor 1/5. Suggest choices for ρ2, V2 and T2

Answer 1

Re1 = Re2, M1 = M2

Re1 = ρ1V1d1/u1
(given that u = CT^1/2)
Re1 = ρ1V1d1/CT^1/2 = ρ1V1d1/C(a1/K)
(given V1/a1 = M1)
Re1 = ρ1M1d1/(C/K)

similarly …
Re2 = ρ2V2d2/(C/K)

Therefore …
ρ1d1 = ρ2d2
(given scale factor is 1/5, d2 = d1/5)

ρ2 = 5 * ρ1

Also for T2 in the wind tunnel means:

V2 = V1 * SQRT(T2/T1)

Question 2

Equation linking T1, T2, V1, V2

Answer 2

(V2/V1)^2 = T2/T1

or

V2 = V1 * SQRT(T2/T1)

Question 3

Equations for Cl and Cd with respect to Cn, Cx and α

Answer 3

Cl = Cn * Cos(α) - Cx * Sin(α)

Cd = Cn * Sin(α) + Cx * Cos(α)

Question 4

Define pathline

Answer 4

The line followed by a fluid element

Question 5

Define streamline

Answer 5

A curve whose tangent at any point is in the direction of the velocity vector

Question 6

When are pathlines and streamlines the same

Answer 6

During steady flow only

Question 7

Equation for vorticity in 2D

Answer 7

w = dv/dx - du/dy

Question 8

Derive from Bernoulli, Cp = 1 - (V/V∞)^2

Answer 8

ρt = ρ + 1/2ρV^2 = ρ∞ + 1/2ρV∞^2

ρ - ρ∞ = 1/2ρ(V∞^2-V^2)

Cp = (ρ - ρ∞) / (1/2ρV∞^2) = 1 - (V/V∞)^2

Question 9

For thin aerofoil theory, equation to calculate moment coefficient, Cm

Answer 9

Cm = - Cl/4

Question 10

How to calculate Cl if you have l (lift per unit area)

Answer 10

Cl = lift per unit area / (1/2ρV^2 * chord length)