FLUIDS: Potential Flow Question - HELP NEEDED

[EngrDelaCruz]

FLUIDS: Potential Flow Question -- URGENT HELP NEEDED

I need to submit this soon and I am way behind in this topic. I would appreciate it a lot if you can help me out figure the answer.

Homework Statement

In a uniform onset flow of 7 m/s parallel with the x axis, a source of strength 19 m2/s per metre is located at the origin (x=0, y=0) and a sink of equal strength is located at (x=2, y=0). Locate the x-axis position of the most upstream stagnation point.

Diagram:

Homework Equations

I think it will be these:

The Attempt at a Solution

Figuring out the stream function:
Psi = (lambda / 2pi)(theta_1 - theta_2)
...
v=7m/s

...

Ugh.. please just help me out on this. It's 5% of the unit. Thanks

 

[Chestermiller]

The velocity of the flow from the 19 m²/s source is $\frac{19}{2π\sqrt{x^2+y^2}}$ and is directed radially outward.

The velocity of the flow from the 19 m²/s sink is $-\frac{19}{2π\sqrt{(x-2)^2+y^2}}$, and is directed radially outward.

According to the problem statement, the stagnation point is along the x-axis (y = 0).

The combined overall velocity along the x-axis is U + ?? + ??. What are the ??'s?