Uniform Flow

The simplest possible potential flow is a uniform flow, $U_\infty=C$. The velocity potential is given by

Figure 4.18: Uniform Flow

$$u = U_\infty = {{\partial \phi} \over {\partial x}},   v = {{\partial \phi} \over {\partial y}} = 0$$ (4.71)

On integration we have

$$\phi = U_\infty x + C$$ (4.72)

where C is the constant of integration, which can be chosen arbitrarily.

The stream function for uniform flow can be easily calculated and is given by,

$$U_\infty = {{\partial \psi} \over {\partial y}},   v = {{\partial \psi} \over {\partial x}} = 0$$ (4.73)

As an exercise the student is asked to write the velocity potential and stream function for flows for which (a) u = 0, v = V and (b) $u = U_\infty cos \alpha$.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney