Page:Lowell Hydraulic Experiments, 4th edition.djvu/72

for the number of buckets,

$$N=3(D+10);$$

for the shortest distance between two adjacent buckets^

$$\omega ={D \over N};$$

for the width of the crown occupied by the buckets,

$$W={{4D} \over N};$$

for the interior diameter of the wheel,

$$d={D={8D \over N}};$$

for the number of guides,

$$n=0.50N\ \mathrm {to} \ 0.75N;$$

for the shortest distance between two adjacent guides,

$$\omega '={d \over n}.$$

Table IV. has been computed by these formulas.

For falls greater than forty feet, the height of the orifices in the circumference of the wheel, should be diminished; the foregoing formulas may, however, still be made use of; thus, supposing that for a high fall, it is determined to make the orifices three fourths of that given by the formula; divide the given power, or quantity of water to be used, by 0.75, and use the quotient in place of the true power, or quantity, in determining the dimensions of the turbine; no modification of the dimensions will be necessary, except that 1/10 of the diameter of the turbine should be diminished to 3/40 of the diameter, to give the height of the orifices in the circumference.

98. It is plain, from the method by which the preceding formulas have been obtained, that they cannot be considered as established, but should only be taken as guides in practical applications, until some more satisfactory are proposed, or the intricacies of the turbine have been more fully unravelled. The turbine has been an object of deep interest to many learned mathematicians, but, up to this time, the results of their investigations, so far as they have been published, have afforded but little aid to Hydraulic Engineers.