Potential Flow Around a Sphere

Comparing a computation for the flow around a sphere from our Panel Flow add-on with exact analytic potential theory is a good test (or verification) of our panel method implementation.


The potential (inviscid) flow around a sphere is equivalent to the superposition of a 3D doublet and a free stream, which reduces to the simple analytic equation:

Cp = 1 - 9/4 cos2(theta)

Cp is the Pressure Coefficent
theta is the angle measured perpendicular to the flow direction


Surface Pressure Coefficient Contours
Surface Pressure Coefficient Contours.

Pressure Coefficient Comparison
Pressure Coefficient comparison between potential flow theory for a sphere and computation.

Notice the excellent agreement between the computation and the theory.

Try For Yourself

The sym project file for this study can be viewed in Caedium or you can investigate this case yourself using our Panel Flow add-on.

The most convenient way to view and edit this case is to use our Professional add-on that combines all the add-ons used during this example.


potential flow around a sphere

Good afternoon,
Could you please provide me with a reference for potential flow around a sphere? I would appreciate it.
best wishes,
Faith Morrison

Potential Flow Around Sphere Reference

My source for the potential flow around a sphere was Low Speed Aerodynamics, Second Edition, Katz and Plotkin, Section 3.12 Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Sphere, pp67-69.