AAE333 Fall 2010
Homework 7
Due: Wed Oct 13 (note Oct Break)
10% bonus if turned in on Friday 10/8/10
1) Determine if the velocity potential φ = 2 x y corresponds to an
incompressible flow.
2) Determine the x, y velocity components corresponding to the velocity
potential φ = 2 x y.
3) Draw lines of constant φ = 2 x y in the square region 0<x<1, 0<y<1.
Draw velocity vectors on this domain.
(this is best done in Matlab using the functions CONTOUR and
QUIVER, as demo’d in class Wed Oct 5)
4) Consider the 2D velocity field u=3 y, v=0:
i. Is this flow incompressible?
ii. Is there a velocity potential describing this flow?
5) The velocity potential φ = x + 0.1 ln(r) , where r = sqrt(x^2+y^2),
corresponds to a uniform free stream flow over a point source (in 2D).
i. Find the x,y velocity components (u,v)
ii. Find the point where u=v=0 (i.e. the stagnation point).
iii. Plot the velocity vectors over a domain from x=-0.2 to x=+0.3
and y=-.3 to +.3.
iv. Try to draw a line separating fluid coming from upstream from that
coming out of the source at x=y=0