Consider the streamlines over a circular cylinder as sketched at the right of Figure 3.26. Single out the first three streamlines flowing over the top of the cylinder. Designate each streamline by its stream function, ψ1, ψ2, and ψ3. The first streamline wets the surface of the cylinder; designate ψ1 = 0. The streamline above that is ψ2, and the next one above that is ψ3. Assume the streamlines start out in the freestream equally spaced. Hence, the volume flow rates between the streamlines are the same. The streamline ψ2 passes through the point (1.2R,π/2) directly above the top of the cylinder. Calculate the location of the point directly above the top of the cylinder through which the streamline ψ3 flows. Comment on the spacing between the streamlines directly above the top.

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Uniform flow = Voor sin 0 K Doublet -K sin 0 2π 11 حل B R A Flow over a cylinder K sin 2π r = Voor sin 0 0 Figure 3.26 Superposition of a uniform flow and a doublet; nonlifting flow over a circular cylinder.