82. The line N O represents the three experiments numbered 90, 91, and 92, made with the regulating gate raised one inch.
An examination of the diagram will show that the velocity corresponding to the maximum coefficient of effect, diminishes with the height of the gate. For heights not less than one fourth of the whole height, this diminution is sufficiently regular; for heights less than one fourth, the experiments are not sufficient to indicate the velocity giving the best effect, but the diminution is evidently more rapid than for greater heights of gate.
Path described by a particle of water in passing through the wheel.
83. As in many other problems in hydraulics, resort is here had to a particular hypothesis, which, at best, is only an approximation to the truth, nevertheless, it may be the means of throwing some light upon the mode in which the water acts upon the wheel.
The particular hypothesis here assumed is this; every particle of water contained in the wheel, situated at the same distance from the axis, moves in the same direction relative to the radius, and with the same velocity. According to this hypothesis, the successive sections in which the same particles of water are found, are in cylindrical surfaces, concentric with the wheel.
Applying this hypothesis to experiment 30, on the Tremont Turbine, let us suppose
AHQ″ = the mean quantity of water discharged through each aperture of the wheel, in cubic feet per second.
AHω = the angular velocity of the wheel.
AHR = the radius of the circle inscribing the inner edges of the buckets, O A figure 3, plate VI.
AHR′ = the radius O B.
AHt = the time occupied by a particle of water in passing from the section A D to the section B G, or, which is the same thing, through the radial distance R′ — R.
AHA = the area of A B C D, in square feet.
AHH = the mean height, in feet, between the crowns of the wheel, between the sections A D and B C.
We have
AH = the volume of water contained between the sections A D and B C.
