When a circular cylinder is placed in a uniform stream, a stagnation point is created on the cylinder. If a small hole is located at this point, the stagnation pressure, $P_{\text{s}\text{t}\text{a}\text{g}},$ can be measured and used to determine the approach velocity, $U,$ as shown below in Fig. A$.$ Assume that this flow can be modeled as the potential flow around a cylinder, $($a$).$ Find the relation between $U$ and $P_{\text{s}\text{t}\text{a}\text{g}}.$

$($b$).$ If the cylinder is misaligned by an angle $10,$ as shown below in Fig. B $,$ the measured pressure is still interpreted as the stagnation pressure, determining the ratio of the true velocity, $U,$ to the predicted velocity, $U^{\text{'}}.$