Problem

A $2$D source of strength $$ located at the origin $(0,0)$ is put into a parallel flow with velocity $u_0$ in positive $x-$axis direction. The velocity potential of the flow is given by

$=u_{0}x+\frac{}{2}ln(\sqrt[\phantom{2}]{x^2+y^2})$

$($a$)$ Derive the velocity vector $v_{x,y}$ for this $2$D flow field. $(6$ of $100$ points$)$

$($b$)$ Compute the stagnation point location $($on the $x-$axis$)$ for a source strength of $=9\frac{m^2}{s}$ and a parallel flow velocity of $u_0=3\mathrm{.}0\frac{m}{s}.$

$(4$ of $100$ points$)$

$($c$)$ Sketch a set of possible streamlines into the upper part of the figure below. Mark the dividing streamline. You may safely assume the flow is symmetric to the $x-$axis.

$(5$ of $100$ points$)$

$($d$)$ Qualitatively sketch the pressure coefficient distribution $C_p(x)$ along the dividing streamline into the lower axes provided below.

$(5$ of $100$ points$)$