An ideal fluid flows past an infinitely long, semicircular "hump" located along a plane boundary, as shown in Fig. P6.58. Far from the hump the velocity field is uniform, and the pressure is \(p_{0}\).

(a) Determine expressions for the maximum and minimum values of the pressure along the hump, and indicate where these points are located. Express your answer in terms of \(ho, U\), and \(p_{0}\).

(b) If the solid surface is the \(\psi=0\) streamline, determine the equation of the streamline passing through the point \(\theta=\pi / 2, r=2 a\).

Figure P6.58

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U. Po