Problem $3$

A counter clock wise rotating cylinder with a radius of R is moving forward in the air. Please use the

superposition of vortex $($Circulation: uniform flow $(\{$:$V_{},P_{})$ and a doublet to simulation the flow

around cylinder ball.

Please find the expression of the doublet strength $($k$).$ Please find the velocity and pressure expressions at

$5$ points $A(=0),B(=\frac{}{4}),C(=\frac{}{2}),D(=\frac{3}{4}),E(=),F(=\frac{5}{4}),G(=\frac{3}{2}),H$

$(=\frac{7}{4}),I(=2)$ on the surface of the cylinder. Please compare the pressure between the top and

bottom surface of the cylinder. Please compare the pressure between the front and back surface of the

cylinder.