Aero 316 - Key Equations

Question 1

Stream function for doublet flow, Psi

Answer 1

-(kappa/2π)*(sin(theta)/r)

Question 2

Velocity potential for doublet flow, ø

Answer 2

(kappa/2π)*(cos(theta)/r)

Question 3

Kappa for stream function is zero for contour of cylinder (r=R)

Answer 3

Kappa = 2π(U∞)R^2

Question 4

u

Answer 4

∂psi/∂y = ∂ø/∂x

Question 5

v

Answer 5

-∂psi/∂x = ∂ø/∂y

Question 6

x

Answer 6

rcos(theta)

Question 7

y

Answer 7

rsin(theta)

Question 8

r

Answer 8

√(x^2 + y^2)

Question 9

Theta

Answer 9

arctan(y/x)

Question 10

Vr

Answer 10

(1/r)(∂psi/∂theta) = ∂ø/dr

Question 11

Vtheta

Answer 11

-∂psi/∂r = (1/r)(∂ø/∂theta)

Question 12

Source strength, ^

Answer 12

2πrVr

Question 13

Kutta-Joukowski Theorem

Answer 13

L’ = rho∞V∞gamma, where gamma is the circulation.

Question 14

Cl

Answer 14

2π(alpha - alpha0), where alpha0 = -1/π*integral_0->π(dz/dx(costheta - 1)dtheta)

Question 15

Centre of pressure for a non-symmetric aerofoil, xp

Answer 15

xac - Cm0/Cl

Question 16

Cmo

Answer 16

(-π/4)(A1-A2)

Question 17

Induced drag coefficient, Cd,i

Answer 17

((Cl)^2)/πe^

Question 18

Drag coefficient (3D), CD

Answer 18

Cd + Cd,i, where Cd is the 2D drag coefficient.

Question 19

Aspect ratio, ^

Answer 19

b/c, where b is wingspan.

Question 20

dCl/dalpha for a given aspect ratio

Answer 20

(πAR(dCl/dalpha)∞)/(πAR + (dCl/dalpha)∞), where ∞ denotes expression evaluated at an aspect ratio of infinity.

Question 21

Skin friction coefficient for flat plate in turbulent flow, cf

Answer 21

0.074/(Re)^1/5

Question 22

Skin friction drag from 2D drag coefficient, cd

Answer 22

cd = 2cf

Question 23

Mn1

Answer 23

M1sin(beta), where beta is the shock angle.

Question 24

Mn2

Answer 24

M2sin(beta-theta), where beta is the shock angle and theta is the deflection angle.

Question 25

Centre of pressure for non-rotating cylinder, Cp

Answer 25

Cp = 1 - 4(sintheta)^2

Question 26

Centre of pressure for a rotating cylinder, Cp

Answer 26

Cp = 1 - 4(sintheta)^2 - (2gammasintheta)/(πRV∞) - (gamma^2)/(4π^2R^2V∞^2)

Question 27

Stagnation point of a Rankine half body, b

Answer 27

^/2πV∞

Question 28

Quarter chord pitching moment coefficient, Cm1/4

Answer 28

Cmac - L(xac - x1/4)

Question 29

Induced angle of attack, alphai

Answer 29

Cl/π^

Question 30

Prandtl-Meyer function

Answer 30

Theta = v(M2) - v(M1)