A two$-$dimensional semi$-$infinite streamlined "body" symmetric with respect to its longitudinal axis is defined by the dividing streamline separating a source flow and a uniform stream. The source of strength $m=45\frac{m^2}{s}$ is placed at the origin of a Cartesian plane and, to give the body incidence with respect to the $x-$axis, the stream is defined by $U=15\frac{m}{s},V=5\frac{m}{s}.$ Given:

${}_c=\frac{m}{2}-Uy,x_s=\frac{m}{2U},y_{\text{m}\text{a}\text{x}}=\frac{m}{2U}$

a$)$ Sketch the outer flow streamline pattern.

$[4$ marks$]$

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Calculate:

b$)$ The incidence angle of the body with respect to the x$-$axis.

$[2$ marks$]$

c$)$ The distance from the leading$-$edge stagnation point to the origin.

$[7$ marks$]$

d$)$ The thickness of the body at the origin $($normal to its longitudinal axis$).$

$[7$ marks$]$