1. Show that: A doublet flow is a physically possible incompressible flow. 2. A doublet flow with K = 10 m/s is at the origin. b) a) Find the equation of the streamline which passes through the point (0, 6). Sketch the resulting flow pattern showing the equipotential lines. Evaluate the total velocity at point (3, 3). 3. Is the flow expressed by: (p= Vox + K ln r) possible for all values of V. and K? Sketch the flow if V = 10 m/s and K = 5 m/s. 4. The Flow over a plane half body is studied by utilizing a free stream of Vo= 5 m/s superimposed on a source at the origin. The body has a maximum width of 2m. Calculate: a) The co-ordinates of the stagnation point. b) The width of the body at the origin. c) The velocity at a point (0.5, /2). 5. A "Rankine Oval" is a Potential-theoretical body found by the superposition of three, two- dimensional flow elements: a source, a sink -of the same strength- and a uniform flow parallel to the line through the source and sink. The uniform flow has a velocity V. in the positive x- direction, the source is of strength (+Q/L) lying at (x = -a, y = 0) and the sink is of strength (-Q/L) lying at (x=+a, y = 0). a. Determine the strength of the source and sink, (Q/L), such that the breadth of the body (measured at its middle, at x = 0) is equal to 2b. b. Determine the velocities u and v of the water particles in the x- and y-directions of the new flow. C. Locate the stagnation points in the flow. d. Determine the Length (L) of the body.