Abstract
In order to predict the performance of a fluid machine from scale-model tests, correction formulae are required. Professor Lewis F. Moody's formula is used for water turbine efficiencies but does not appear to be accepted for pumps; Pfleiderer† states that it is not practicable to use Reynolds number; and Wislicenus‡ does not give a formula for scale correction but states that efficiency increases slowly with size and speed. For cavitation, the only general formula is Thoma's parameter§ from which is developed suction specific speed. Wislicenus, Watson, and Karassik‖ rely entirely on suction specific speed and state that the influence of Reynolds number can be neglected.
It is suggested that both the total head loss—given by (1 – η) where η denotes the efficiency—and suction side loss (cavitation) may be treated similarly and analysed according to the Reynolds number. Examples of centrifugal pump efficiencies and cavitation characteristics are analysed, and the resulting curves are found to have the same shape as corresponding portions of the original Reynolds curve for pipe friction. The losses in a fluid machine are thus represented by the friction loss of a certain length of pipe. Extrapolation for sizes and speeds beyond the known field of tests can then be made by analogy with the pipe friction curve.
From the foregoing considerations, the author suggests that the Moody formula for the losses: (1–η)∝ 1/D0·25H0·1—where D and H refer to diameter and head respectively—should be replaced by (1 – η)∝ (D✓H)–x where x varies between 0·2 and 00·3, according to Reynolds number. A similar relation is derived for cavitation.
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