Rankine body (or Rankine Oval). It becomes a circular cylinder as the source-sink pair
approach each other. Take a plane source of strength m at point (-a, 0), a plane sink of equal
strength at (a, 0), and superpose a uniform stream with a velocity magnitude of U directed
along the x-axis.
Assumption: incompressible 2D potential flows
1) For uniform flow, please derive the velocity components u and v, and the stream function
Ψ. (15 points)
2) For source and sink, please derive radial velocity component $u_r$ and stream function Ψ.
Also please derive the velocity components u and v in Cartesian coordinates based on
$u_r$. (20 points)
3) For the superposition flow mentioned in this question, please derive the velocity
components and stream function. (20 points)
4) Please make a MATLAB or python code to visualize the flows in this question.
Requirements: You need to label the sink and source location in the plot. You need to
provide both streamline plot and contour plot for the stream function. (15 points)
• X ranges from -3 to 3 with a step of 0.05
• Y ranges from -2 to 2 with a step of 0.05
• $U = 2$ m/s
• $m = 1$
• $a = -1.5$
