Potential flow against a flat plate (Fig. P6.51a) can be described with the stream function [ psi=A

Question:

Potential flow against a flat plate (Fig. P6.51a) can be described with the stream function

\[ \psi=A x y \]

where \(A\) is a constant. This type of flow is commonly called a stagnation point flow since it can be used to describe the flow in the vicinity of the stagnation point at \(O\). By adding a source of strength \(m\) at \(O\), stagnation point flow against a flat plate with a "bump" is obtained as illustrated in Fig. P6.51b. Determine the relationship between the bump height, \(h\), the constant, \(A\), and the source strength, \(m\).

Figure P6.51