1. A 2-D system consists of two sinks/sources, one is located at the origin, and the other is located at the point (4,0). Each object can be a sink, or a source, or turned off. They can be used to move a given fluid element to a pre-specified location: when the object is on, a fluid element follows a stream line created by the object. All the flows are in the horizontal plane.

(a). Sketch the velocity field (and, thus, trajectories of the fluid elements) when only one source is on, and then when two sources (with the same strength) are on.

(b). Let the source at the origin be on, with the strength m, and the other be off. If the pressure at point (1,1) is p1, compute the pressure p1 at the point (3,3).

(c). Determine the algorithm to deliver the fluid element from point (-1,3) to (5,5).

Hint: don't use both source/sinks at the same time!

(d). Let the source/sink at the origin be a source with strength m. Determine the strength of the other source/sink if the point (-8,0) is stationary. (Note: now BOTH are active.) Is it possible to make point (3,3) stationary?