Consider stagnation point potential flow over a flat plate as shown below on the left.

The stream function for this flow is given by

$=$Axy

where $A$ is a constant. The origin $O$ here is the stagnation point. $($Note You can use the stream function above to prove this. You may verify this if you desire additional practice$).$ To this stagnation point flow we add a source of strength A which generates potential flow over bump as shown below on the right. This would simulate flow inside a heat exchanger, for example, when there is some form of mineral deposition. Another example would be a jet exhaust impinging on an object during take off.

$($a$)$ Determine the bump height $h.$

$($b$)$ Determine the surface streamline ${}_s.$

$($c$)$ Write a script to plot the streamlines. Use $A==1.$ Plot ${}_s$ using a different color. Highlight the location of the stagnation point.

Hint: ${}_s$ has to pass through the stagnation point.