4.3 A two-dimensional source is located at (1, 0) and another one of the same strength is at (-1,
0). Draw to scale the velocity vectors at the following locations: (0, 0), (0, 1), (0, -1), (0, -2),
and (1, 1). Use a scale such that 1 in. is the magnitude of the velocity produced by either source at
a distance of 1 in. from its location. Use the results of problem 3.12.
4.4 Determine the velocity potential and stream function for a source located at (1, 0). Write the
equation for the velocity potential for the source system of problem 4.3.
4.5 Determine the equation for the velocity on the surface x = 0 in the flow given in problem 4.3.
Find an equation that gives the pressure along this surface relative to the pressure P at a great
distance from the sources, where the fluid is stationary. Neglecting hydrostatic effects, what is the
force on one side of the surface due only to the flow? (Assume that the surface is infinite in extent
in the y direction and of width b in the z direction.)
4.6 Find the point of maximum velocity on the surface of problem 4.5. What can be said about the
relative magnitude of the pressure at this point?