Problem 6.113 - Problem 6.113 [Difficulty: 4] Given:...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Problem 6.113 [Difficulty: 4] Given: Complex function Find: Show it leads to velocity potential and stream function of irrotational incompressible flow; Show that df/dz leads to u and v Solution: Basic equations: u y ψ = v x ψ = u x φ = v y φ = First consider x f x z z f d d = 1 z f d d = z f d d = (1) and also y f y z z f d d = i z f d d = i z f d d = (2) Hence 2 x f 2 xx f = zz f d d d d = 2 z f d d 2 = and 2 y f 2 yy f = i z i z f d d d d = 2 z f d d 2 = Combining 2 x f 2 2 y f 2 + 2 z f d d 2 2 z f d d 2 = 0 = Any differentiable function f(z) automatically satisfies the Laplace
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online