Radial equilibrium

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Radial equilibrium

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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] and before a rotor [turbine] respectively:

The definition of total pressure in section 2 differentiated with respect to r plus above equation yield:

With the blade work according to Euler the equation becomes:

With the following boundary conditions and a given cu2(r)-specification the solution of the differential equation gives a cm2(r)-distribution and therefore the complete velocity triangles at every span.

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