These approximate equations, which are derived purely from experiment, do not differ greatly from those obtained by the rough theory given above. The theory helps to explain the reason for the form of the empirical results.
(W. C. U.)
[1] Except where other units are given, the units throughout this article are feet, pounds, pounds per sq. ft., feet per second.
[2] Journal de M. Liouville, t. xiii. (1868); Mémoires de l’Académie, des Sciences de l’Institut de France, t. xxiii., xxiv. (1877).
[3] The following theorem is taken from a paper by J. H. Cotterill, “On the Distribution of Energy in a Mass of Fluid in Steady Motion,” Phil. Mag., February 1876.
[4] The discharge per second varied from .461 to .665 cub. ft. in two experiments. The coefficient .435 is derived from the mean value.
[5] “Formulae for the Flow of Water in Pipes,” Industries (Manchester, 1886).
[6] Boussinesq has shown that this mode of determining the corrective factor α is not satisfactory.
[7] In general, because when the water leaves the turbine wheel it ceases to act on the machine. If deflecting vanes or a whirlpool are added to a turbine at the discharging side, then v1 may in part depend on v2, and the statement above is no longer true.