Assume that the flow around the long circular cylinder of Fig. P6.59 is nonviscous and incompressible. Two

Question:

Assume that the flow around the long circular cylinder of Fig. P6.59 is nonviscous and incompressible. Two pressures, $p_{1}$ and $p_{2}$, are measured on the surface of the cylinder, as illustrated. It is proposed that the free-stream velocity, $U$, can be related to the pressure difference $\Delta p=p_{1}-p_{2}$ by the equation

\[ U=C \sqrt{\frac{\Delta p}{ho}} \]

where $ho$ is the fluid density. Determine the value of the constant $C$. Neglect body forces.

Figure P6.59