Differential equations of motion for (a) the rotating parts of the pump and prime mover, and (b) the fluid in the pipes are derived. Methods of integrating the equations are discussed for the case of an assumed rigid fluid column and for the elastic fluid column. A hitherto unpublished solution for the elastic-column problem is described. Complete characteristics diagrams for several pumps are given. Solutions by different methods are compared and examples for actual installations shown.

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