The conditions under which rothalpy is conserved are investigated by means of the energy and moment-of-momentum equations for unsteady flow of a viscous, compressible fluid. Differential and integral equations are given for the total enthalpy and rothalpy in both stationary and rotating coordinates. From the equations in rotating coordinates it is shown that rothalpy may change due to: (1) pressure fluctuations caused by flow unsteadiness in the rotating frame; (2) angular acceleration of the rotor; (3) work done by viscous stresses on the relative flow in the rotating frame; (4) work done by body forces on the relative flow; (5) changes in entropy due to viscous dissipation and heat transfer. Conclusions of this investigation are compared with those of previous authors, some of whom have stated that rothalpy is conserved even in viscous flows. A modified Euler’s turbomachine equation, which includes viscous effects, is derived and errors in previous derivations noted.

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