Problem

Consider the upstream half (x < 0) of the flow field of Prob. 11–58 (flow over a circu...

Consider the upstream half (x < 0) of the flow field of Prob. 11–58 (flow over a circular cylinder). We introduce a parameter called the stream function ψ. bwhich is constant along streamlinesin two-dimensional flows such as the one being considered here (Fig. P11–60) The velocity field of Prob. 11–58 corresponds to a stream function given by

(a) Setting ψto a constant, generate an equation for a streamline. (Hint: Use the quadratic rule to solve for r as a function of θ.)

(b) For the particular case in which V = 1.00 m/s and cylinder radius a = 10.0 cm, plot several streamlines in the upstream half of the flow (90°< θ < 270°). For consistency, plot in the range –0.4 m< x < 0 m, – 0.2 m < y < 0.2 m, with stream function values evenly spaced between –0.16 m2/s and –0.16 m2/s.