Potential Flows

flow	source plus uniform flow

U

1.

A

1.

a

1.

b

0.5

α

4.

n

1.25

γ

1.

h

1.

contours

20

style

Automatic

None

A potential flow is characterized by a velocity field that is the gradient of a scalar function, the velocity potential. This velocity field is irrotational, because the curl of a gradient is identically zero. Velocity potentials are obtained as solutions of Laplace's equation, most conveniently in the complex plane. Some applications include water-wave propagation, airfoils, electrostatics, and heat flow. The equations can be used for modeling both stationary and nonstationary flows.

Potential flows for different cases are shown. As described in the references,

U

is the velocity field and

γ

is the strength of the source, while

n

,

α

,

A

,

a

,

b

, and

h

are other hydrodynamic parameters in the model.