Page:Lowell Hydraulic Experiments, 4th edition.djvu/58

 the wheel preponderated. In 43, the weight was the least that would cause the scale to lower when the bell crank was placed horizontally, and then left free; on the other hand, in experiment 44, the weight was the greatest that would allow the scale to be raised under the same circumstances; that is to say, in 43, the weight represents the force exercised by the water against the wheel, plus the friction of the entire apparatus, and in 44, the weight represents the same thing, minus the friction; the difference of the weights, or 4213.38 − 3946.38 = 267 pounds, represents double the friction, and the true force exercised by the water against the wheel, is represented by the weight

$${{4213.38 + 3946.38} \over {2}} = 4079.88\ \mathrm{pounds.}$$

This weight acted at a distance from the centre of the wheel, equal to the effective length of the brake, or 10.827778 feet (art. 50).

The radius of the turbine, at the outer extremities of the buckets, is 4.146 feet (art. 35), consequently, the equivalent force acting tangentially at the outer extremities of the buckets, was

$${{4079.88 \times 10.827778} \over {4.146}} = 10655.1\ \mathrm{pounds.}$$

78. The line E F represents the experiments numbered 77, 78, and 79, made with the gate raised 9.96 inches, or about 87 per cent. of the full height. By a reference to the table of experiments, it will be seen that, although the regulating gate was lowered 13 per cent., the quantity of water discharged by the wheel was diminished less than one per cent.

79. The line G H represents the experiments numbered from 51 to 64, inclusive, made with the gate raised 8.55 inches, or about three fourths of the full height.

80. The line I K represents the experiments numbered from 65 to 76, inclusive, made with the gate raised 5.65 inches, or nearly a half of the full height.

81. The line L M represents the experiments numbered from 80 to 87, inclusive, made with the gate raised 2.875 inches, or one fourth of its full height. Experiments 88 and 89 were made with the same height of gate, but with the wheel held fast by the brake; the force exerted by the wheel at the distance 10.827778 feet, independent of friction, was

$${{1195.06 + 1054.25} \over 2} = 1124.65\ \mathrm{pounds.}$$