The velocity potential [ phi=-kleft(x^{2}-y^{2} ight) quad(k=text { constant }) ] may be used to represent the flow against an infinite plane boundary, as illustrated

The velocity potential

\[ \phi=-k\left(x^{2}-y^{2}\right) \quad(k=\text { constant }) \]

may be used to represent the flow against an infinite plane boundary, as illustrated in Fig. P6.35. For flow in the vicinity of a stagnation point, it is frequently assumed that the pressure gradient along the surface is of the form

\[ \frac{\partial p}{\partial x}=A x \]

where \(A\) is a constant. Use the given velocity potential to show that this is true.

Figure P6.35