U∞ h y h г Ꮖ
We can model potential flow over a jellybean by using a source (Q), vortex (Γ), and sink (−Q)
placed on the x axis as shown below. When combined with uniform flow (U∞), the superimposed
elementary flows will model flow over a closed shape that resembles a jellybean. For the numerical
parts below, use U∞ = 5m/s, Γ = 10m2/s, Q = 8m2/s, and h = 0.5m.
a) Write the complex potential, F (z), for this flow, in terms of z and the given parameters (not
numerical values).
b) Write the equation for the complex velocity, w(z), again in terms of the given parameters.
c) Determine the location of the stagnation points in this flow, using the given numerical values.
You should find three points, with two at the leading/trailing edge of the closed shape.
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