A flow field is formed by combining a uniform flow in the positive x direction, with U =10 m/s, and a counterclockwise vortex, with strength K = 16 π m2/s, located at the origin. Obtain the stream function, velocity potential, and velocity field for the combined flow. Locate the stagnation point(s) for the flow. Plot the streamlines and potential lines. ( Hint: Use the Excel workbook of Example 6.10.)

Example  6.10 VELOCITY POTENTIAL

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Consider the flow field given by w =ar -ay, where a = 3s.Show that the flow is inotational. Determine the velocity poten- tial for this flow. Given: Incompressible flow field with y =a -ay", where a=3s-!. Find: (a) Whether or not the flow is irmotational. (b) The velocity potential for this flow. Solution: If the flow is inotational, Vy =0. Checking for the given flow, (ar -ay) +ar-ay") =2a-2a =0 Consider the flow field given by w =ar -ay, where a = 3s.Show that the flow is inotational. Determine the velocity poten- tial for this flow. Given: Incompressible flow field with y =a -ay", where a=3s-!. Find: (a) Whether or not the flow is irmotational. (b) The velocity potential for this flow. Solution: If the flow is inotational, Vy =0. Checking for the given flow, (ar -ay) +ar-ay") =2a-2a =0