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

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

On integration we have
$\displaystyle \phi = U_\infty x + C$ (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,

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