y feet fall is required?_ Formula:

33,000 x horsepower required
(C) Head in feet = ------------------------------
Cu. Ft. per minute x 62.5

Since a theoretical horsepower is only 75 per cent efficient, he would
require 10 x 4/3 = 13.33 theoretical horsepower of water, in this
instance. Substituting the values of the problem in the formula, we
have:

33,000 x 13.33
Answer: Head = ---------------- = 17.6 feet fall required.
400 x 62.5

_What capacity of wheel would this prospect (400 cubic feet of water a
minute falling 17.6 feet, and developing 13.33 horsepower) require?_

By referring to the table of velocities, we find that the velocity for
17.5 feet head (nearly) is 33.6 feet a second. Four hundred feet of
water a minute is 400/60 = 6.67 cu. ft. a second. Substituting these
values, in formula (B) then, we have:

Answer: Capacity of wheel =

144 x 6.67
---------- = 28.6 square inches of water.
33.6

_Quantity of Water_

Let us take still another problem which the prospector may be called
on to solve: _A man finds that he can conveniently get a fall of 27
feet. He desires 20 actual horsepower. What quantity of water will be
necessary, and what capacity wheel?_

Twenty actual horsepower will be 20 x 4/3 = 26.67 theoretical
horsepower. Formula:

33,000 x Hp. required
(D) Cubic feet per minute = ---------------------
(Head in feet x 62.5)

Substituting values, then, we have:

Cu. ft. per minute =

33,000 x 26.67
-------------- = 521.5 cubic feet a minute.
27 x 62.5

A head of 27 feet would give this stream a velocity of 41.7 feet a
second, and, from formula (B) we find that the capacity of the wheel
should be 30 square inches.

It is well to remember that the square inches of wheel capacity does
not refer to the size of pipe conveying water from the head to the
wheel, but merely to the actual nozzle capacity provided by the wheel
itself. In small installations of low head, such as above a penstock
at least six times the nozzle capacity should be used, to avoid losing
effective head from friction. Thus, with a nozzle of 30 square inches,
the penstock or pipe should be 180 square inches, or nearly 14 inches
square inside measurement. A larger penstock would be still better.

CHAPTER IV

THE WATER WHEEL AND H