Aero 316 - Key Equations Flashcards
Stream function for doublet flow, Psi
-(kappa/2π)*(sin(theta)/r)
Velocity potential for doublet flow, ø
(kappa/2π)*(cos(theta)/r)
Kappa for stream function is zero for contour of cylinder (r=R)
Kappa = 2π(U∞)R^2
u
∂psi/∂y = ∂ø/∂x
v
-∂psi/∂x = ∂ø/∂y
x
rcos(theta)
y
rsin(theta)
r
√(x^2 + y^2)
Theta
arctan(y/x)
Vr
(1/r)(∂psi/∂theta) = ∂ø/dr
Vtheta
-∂psi/∂r = (1/r)(∂ø/∂theta)
Source strength, ^
2πrVr
Kutta-Joukowski Theorem
L’ = rho∞V∞gamma, where gamma is the circulation.
Cl
2π(alpha - alpha0), where alpha0 = -1/π*integral_0->π(dz/dx(costheta - 1)dtheta)
Centre of pressure for a non-symmetric aerofoil, xp
xac - Cm0/Cl
Cmo
(-π/4)(A1-A2)
Induced drag coefficient, Cd,i
((Cl)^2)/πe^
Drag coefficient (3D), CD
Cd + Cd,i, where Cd is the 2D drag coefficient.
Aspect ratio, ^
b/c, where b is wingspan.
dCl/dalpha for a given aspect ratio
(πAR(dCl/dalpha)∞)/(πAR + (dCl/dalpha)∞), where ∞ denotes expression evaluated at an aspect ratio of infinity.
Skin friction coefficient for flat plate in turbulent flow, cf
0.074/(Re)^1/5
Skin friction drag from 2D drag coefficient, cd
cd = 2cf
Mn1
M1sin(beta), where beta is the shock angle.
Mn2
M2sin(beta-theta), where beta is the shock angle and theta is the deflection angle.
Centre of pressure for non-rotating cylinder, Cp
Cp = 1 - 4(sintheta)^2
Centre of pressure for a rotating cylinder, Cp
Cp = 1 - 4(sintheta)^2 - (2gammasintheta)/(πRV∞) - (gamma^2)/(4π^2R^2V∞^2)
Stagnation point of a Rankine half body, b
^/2πV∞
Quarter chord pitching moment coefficient, Cm1/4
Cmac - L(xac - x1/4)
Induced angle of attack, alphai
Cl/π^
Prandtl-Meyer function
Theta = v(M2) - v(M1)
