Page 807 - Advanced_Engineering_Mathematics o'neil

23.4 Models of Plane Fluid Flow 787

9. Analyze the flow having complex potential with K and a positive constants. Show that f mod-
2
els an irrotational flow around a cylinder 4x + 4(y −
1 ib
2
2
f (z) = K z + + Log(z) a) = a with a flat boundary along the y-axis. Sketch
z 2π
some equipotential curves and streamlines.
with k and b as nonzero, real numbers. Sketch some
equipotential curves and streamlines. 11. Use Blasius’s theorem to show that the force per unit
width on the cylinder in Problem 10 has vertical com-
10. Analyze the flow having potential √ 2
ponent of 2 3πρaK with ρ as the constant density
√

√ 2z − ia 3 of the fluid.
f (z) = iKa 3Log √
2z + ia 3

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