Inviscid ( μ = 0) 2. Incompressible 3. Irrotational • It describes the flow around streamlined objects far away from the object. (In the near field the boundary layer theory is used) • This type of problems deals with more than one velocity component, and function in more than one independent variable.
Potential Flow • To solve them in an easy way conformal mapping is used. • So instead of solving N-S equations to get the velocity profile, complex potential is used. • w(z) = ϕ (x, y) + i ψ (x, y) • Where: 1. ϕ (x, y) is the velocity potential 2. ψ (x, y) is the stream line function 3. z = x + i y = r e i θ = r cos θ + i sin θ • The three forms of z are equivalent to each other, choose the one that makes your solution easier !!
Potential Flow • For a given function to represent a potential flow: 1. Cauchy-Riemann conditions should be verified 2. Ψ = constant, represent the solid surface.