Problem $9$

Imagine a flow composed of a vortex added to a cylinder of radius $0$ in a uniform flow of free

stream velocity U:

$=0$

$2$

$+$

$2$

a$)$ Determine expressions for the velocity components. Show detailed work.

b$)$ Derive an expression for the pressure coefficient Cp$.$ The pressure coefficient is defined as

$$p $=$

$1$

$22$

Here, Take P as the pressure at the surface. Hint : Use Bernoulli$$s formula $.$ Show detailed work

c$)$ Derive an expression for the lift force per unit depth into the page. Show detailed work. Pleae show detailed work