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Ch. 9: Measurements of FLowin Water

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128              MEASUREMENT OF FLOWING WATER.
gineers have been compelled to rely for correctness of calculated results on the application of a combination of a few known laws with experimental data, which latter, though all-important, have been too restricted for the de­duction of a reliable mathematical theory.
The formulas, in terms of dimensions of cross section and slope, are based upon the supposition of either " per­manent " or " uniform " motion. Permanent motion ap­proaches the condition of streams, permits changes of cross section and slope of the water-surface, excepting sudden bends, causing eddies and undulations, but de­mands that the discharge from the different sections should be identical. Uniform motion, in addition, requires an invariable cross section and constant slope of the fluid-surface. The general formulas based on permanent mo­tion differ from those restricted to uniform motion, " by taking into account changes of living force produced by changes of cross section at the different points." * If there are no variations, the difference between the for­mulas disappears.
Chezy considered that the resistances encountered by water in uniform motion were in direct proportion to the length of the wetted perimeter, to the length of the chan­nel, and to the square of the mean velocity ; from which he deduced the formula,
The equation indicates the relation of the mean veloci­ty to the slope and the mean hydraulic radius. The value of the coefficient c has been empirically demonstrated to
* Humphreys and Abbot, Mississippi Report, p. 207.
Ch. 9: Measurements of FLowin Water Page of 331 Ch. 9: Measurements of FLowin Water
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