Please answer all parts...

Consider the potential flow field obtained by super$-$imposing a uniform flow $U_{}$ in the $x$ direction

with a source of strength $K$ placed at $(x,y)=(-a,0)$ and a sink of equal strength $($i$.$e$.,-K$ placed at

$(x,y)=(+a,0).$ See the figure below for reference.

a$)$ Derive the expression of the velocity potential function $.$

b$)$ Derive the components of the velocity field: $V=ui+vj.$

c$)$ With the aid of a computer program, plot the velocity field and discuss it$.$ Let $U_{}=1\frac{m}{s},$

$a=0\mathrm{.}5m$ and $K=1\frac{m^2}{s}.$

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Consider the potential flow field obtained by super$-$imposing a uniform flow $U_{}$ in the $x$ direction

with a source of strength $K$ placed at $(x,y)=(-a,0)$ and a sink of equal strength $($i$.$e$.,-K$ placed at

$(x,y)=(+a,0).$ See the figure below for reference.

a$)$ Derive the expression of the velocity potential function $.$

b$)$ Derive the components of the velocity field: $V=ui+vj.$

c$)$ With the aid of a computer program, plot the velocity field and discuss it$.$ Let $U_{}=1\frac{m}{s},$

$a=0\mathrm{.}5m$ and $K=1\frac{m^2}{s}.$

Important:

Submit the script used to produce the figure along with the assignment.it the script used to produce the figure along with the assignment