Consider the two-dimensional air flow around the corner, as shown in Fig. P6.33. The (x) - and (y)-direction velocities are [ u=frac{v_{0}}{L} sin mathrm{h}left(frac{x}{L} ight)

Consider the two-dimensional air flow around the corner, as shown in Fig. P6.33. The \(x\) - and \(y\)-direction velocities are

\[ u=\frac{v_{0}}{L} \sin \mathrm{h}\left(\frac{x}{L}\right) \cosh \left(\frac{y}{L}\right) \]

and

\[ v=-\frac{v_{0}}{L} \cosh \left(\frac{x}{L}\right) \sin \mathrm{h}\left(\frac{y}{L}\right) \]

respectively. Assume constant density, steady flow, negligible gravity, and inviscid flow. Find \(p(x, y)\).

Figure P6.33

0 0 v(x, L) L u (L,y) x