Gothert Rule

The aerodynamic coefficients of a body in three-dimensional compressible flow are obtained as follows. The geometry of the given body is transformed in such a way that its lateral and normal dimensions (both

in y and z directions) are multiplied by 11 — Ml |. If the flow is subsonic, compute the incompressible

flow about the transformed body; if the flow is supersonic, compute the field with Ml = [ї about the transformed body. The aerodynamic coefficients of the given body in given flow, follow from transformed flow with Equation (9.115).

Gothert rule can be applied to two-dimensional flows also (stated as version III of the Prandtl-Glauert rule).

It is exact in the framework of linear theory, whereas the Prandtl-Glauert rule is only approximate. For thicker bodies, when there is doubt about the accuracy with P-G rule, Gothert rule should be used even though it is tedious.

The coefficient of pressure is:

Cp = -2 —.

p V

V CO

The error involved in the pressure coefficients ratio is:

That is why the P-G rule, though approximate, can be used quite satisfactorily up to t/c = 15% (because the error is less). Gothert rule is still superior and is applicable not only to flow past bodies but also to flow through ducts where the diameter is small.