Page:Lowell Hydraulic Experiments, 4th edition.djvu/70

 the wheel, should be about one half of that due to the fall acting upon the wheel; and by comparison of experiments 74 and 84, it will be seen that, with this height of gate, and with this velocity, the coefficient of useful effect must be near 0.50.

This example shows, in a strong light, the well-known defect of the turbine, viz., giving a diminished coefficient of useful effect, at times when it is important to obtain the best results. One remedy for this defect would be, to have a spare turbine, to be used when the fall is greatly diminished; this arrangement would permit the principal turbine to be made nearly of the dimensions required for the greatest fall. As at other heights of the water, economy of water is usually of less importance, the spare turbine might generally be of a cheaper construction.

95. To lay out the curve of the buckets, the author makes use of the following method.

Referring to plate III, figure 1, the number of buckets, $$N$$, having been determined by the preceding rules, set off the arc $gi = {\pi D} \over N$.

Let $$\omega = gh$$, the shortest distance between the buckets; $$t =$$ the thickness of the metal forming the buckets.

Make the arc $$gk=5\omega$$. Draw the radius $$Ok$$, intersecting the interior circumference of the wheel at $$l$$; the point $$l$$ will be the inner extremity of the bucket. Draw the directrix $$lm$$ tangent to the inner circumference of the wheel. Draw the arc $$on$$, with the radius $$\omega + t$$, from $$i$$, as a centre; the other directrix, $$gp$$, must be found by trial, the required conditions being, that, when the line $$ml$$ is revolved round to the position $$gt$$, the point $$m$$ being constantly on the directrix $$gp$$, and another point at the distance $$mg=rs$$, from the extremity of the line describing the bucket, being constantly on the directrix $$ml$$, the curve described shall just touch the arc $$no$$. A convenient line for a first approximation, may be drawn by making the angle $$Ogp = 11^\circ$$. After determining the directrix according to the preceding method, if the angle $$Ogp$$ should be greater than 12°, or less than 10°, the length of the arc $$gk$$ should be changed, to bring the angle within these limits.

The curve $$gss's''l$$, described as above, is nearly the quarter of an ellipse, and would be precisely so, if the angle $$gml$$ was a right angle; the curve may be readily described, mechanically, with an apparatus similar to the elliptic trammel; there is, however, no difficulty in drawing it by a series of points, as is sufficiently obvious.