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Basis of this is the balance of pressure and centrifugal forces under the following assumptions:

•the flow is rotationally symmetric

•friction is neglected

•the streamlines are axis-parallel and have no inclination

The radial balance equation is given here for a section behind an impeller [pump, compressor, fan], i.e., x = 2, and before a rotor [axial turbine], i.e, x = 1:

The definition of total pressure in section x differentiated w.r.t. r plus above equation yield:

With the blade work according to Euler the equation becomes:

With the following boundary conditions and a given cux(r)-specification the solution of the differential equation gives a cmx(r)-distribution and therefore the complete velocity triangles at every span. The pre-swirl cu·r·ω is considered by pswx.

From the velocity triangles the degree of reaction can be determined by the following equation: