Page:Lowell Hydraulic Experiments, 4th edition.djvu/88

 118. The results of the experiments in table VI., are represented by a system of coödrdinates at figure 1, plate IX.;— the relative velocities, given in column 20, are taken for the abscissas, and the corresponding ratios of the useful effects to the powers expended, given in column 17, are taken for the ordinates. The numbers on the figure refer to the experiments in table VI., which the several points represent;— the points not numbered represent some experiments not reported, in consequence of an imperfection in the gauge of the quantity of water discharged, owing to a defective arrangement of the grating. These experiments have been corrected by a comparison with those that are reported; notwithstanding this correction, however, they ought not to be considered as of equal value with those reported in table VI. In the figure, the points representing the latter experiments, are connected by full lines; the points representing the experiments considered imperfect, are connected by broken lines. The line A B represents the experiments reported, that were made with the regulating gate fully raised; the line C D, the experiments with the gate raised three quarters of its full height; E F, the experiments with the gate raised a half, and G H, the experiments with the gate raised one quarter of its full height. It will be seen that the maximum coefficient of effect, with the gate fully raised, is given, when the outside of the wheel is moving with a velocity equal to about sixty-seven per cent. of that due to the fall acting upon the wheel, at which velocity, the useful effect is very nearly eighty per cent. of the total power of the water. The coefficient of effect diminishes rapidly as the regulating gate is lowered, and the maximum is also found at a slower speed; thus, when the gate is raised three inches, or one quarter of its full height, the maximum coefficient of effect is thirty-eight per cent. of the power expended; which is given when the outside of the wheel is moving with a velocity about one half of that due to the fall acting upon the wheel.

119. A B C D, figure 2, plate IX., represents the path of the water as it passed through one of the apertures of the wheel, in experiment 30, according to the hypothesis in art. 83; the steps in the calculation for which, are given in table VII. In the formula $$O = {{R' \omega A H} \over {Q''}},$$ we have for this case,