Page:Lowell Hydraulic Experiments, 4th edition.djvu/66

consequently,

$$138.1892=7.68692\times 8.0202{\sqrt {12.903}}C,$$

$$\mathrm {or} \ C=0.624.$$

By rule 2, we have $H=0.10D$:

then $HD=0.10D^{2}$,

and $Q=HDV'=0.10D^{2}C{\sqrt {2gh}}$,

or $Q=0.5D^{2}{\sqrt {h}}$.

Calling the weight of a cubic foot of water 62.33 pounds avoir, we have

$P={{0.75\times 62.33} \over 550}Qh,$

$\mathrm {or} \ P=0.085\,Qh;$

or, substituting the value of Q just found,

$P=0.0425D^{2}h{\sqrt {h}},$

from which we may deduce

$D=4.85{\sqrt {P \over {h{\sqrt {h}}}}}.$

91. The number of buckets is, to a certain extent, arbitrary, and would usually be determined by practical considerations: some of the ideas to be kept in mind are the following.

The pressure on each bucket is less, as the number is greater; the greater number will therefore permit of the use of the thinner iron, which is important, in order to obtain the best results. The width of the crowns will be less for a greater number of buckets: a narrow crown appears to be favorable to the useful effect, when the gate is only partially raised. As the spaces between the buckets must be proportionally narrower for a larger number of buckets, the liability to become choked up, either with anchor ice, or other substances, is increased. The amount of power lost by the friction of the water against the surfaces of the buckets, will not be materially changed, as the total amount of rubbing surface on the buckets, will be nearly constant for the same diameter: there will be a little less on the crown, for the larger number. The cost of the wheel will probably increase with the number of buckets. The thickness and quality of the iron, or other metal intended to be used for the buckets, will sometimes be an element. In some waters, wrought iron is rapidly corroded.