C$.$ For the fluid velocity field defined by doublet of strength $\backslash (\backslash$mathrm$\{$K$\}=9\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$sec$\}(\backslash$mathrm$\{$so$\}\backslash$psi$=-9*\backslash$sin $\backslash$Theta $/\backslash$mathrm$\{$r$\})\backslash )$ :

i$.$ Determine expressions for the radial and tangential velocities.

ii$.$ Find an equation for the streamline through $\backslash (\backslash$theta$=90\backslash )$ degrees, $\backslash ($ r$=3\backslash ).$

iii. Sketch the streamline. Feel free to create the sketch using excel or Matlab$/$other; note that you need to complete one cycle $($go through $360$ degrees$).$

iv$.$ Calculate the fluid speed at the following angles and then add velocity vectors to your streamline at $30$ degrees, $45$ degrees, $95,130$ degrees, $150$ degrees. $($ok to use excel, just provide a screenshot$).$

v$.$ Add arrows to the streamline indicating flow direction.

D$.$ For the same doublet as in C

i$.$ Find an equation for the streamline through $\backslash (\backslash$Theta$=90\backslash )$ degrees, $\backslash ($ r$=6\backslash ).$

i$.$ Sketch the streamline. You can add it to the graph in problem C if you want.

ii$.$ Calculate the fluid speed at the following angles and then add velocity vectors to your streamline at $30$ degrees, $45$ degrees, $135$ degrees, $150$ degrees.

iii. Add arrows to the streamline indicating flow direction.