e laws which lie at the root and govern the whole question
under present consideration. Water obeys the laws of gravity, exactly like
every other body; and the velocity with which any quantity may be falling
is an expression of the full amount of work it contains. By a sufficiently
accurate practical rule this velocity is eight times the square root of the
head or vertical column measured in feet. Velocity per second = 8 sqrt
(head in feet), therefore, for a head of 100 ft. as an example, V = 8 sqrt
(100) = 80 ft. per second. The graphic method of showing velocities or
pressures has many advantages, and is used in all the following diagrams.
Beginning with purely theoretical considerations, we must first recollect
that there is no such thing as absolute motion. All movements are relative
to something else, and what we have to do with a stream of water in a
turbine is to reduce its velocity relatively to the earth, quite a
different thing to its velocity in relation to the turbine; for while the
one may be zero, the other may be anything we please. ABCD in Fig. 1
represents a parallelogram of velocities, wherein AC gives the direction of
a jet of water starting at A, and arriving at C at the end of one second or
any other division of time. At a scale of 1/40 in. to 1 ft., AC represents
80 ft., the fall due to 100 ft. head, or at a scale of 1 in. to 1 ft., AC
gives 2 ft., or the distance traveled by the same stream in 1/40 of a
second. The velocity AC may be resolved into two others, namely, AB and AD,
or BC, which are found to be 69.28 ft. and 40 ft. respectively, when the
angle BAC--generally called _x_ in treatises on turbines--is 30 deg. If,
however, AC is taken at 2 ft., then A B will be found = 20.78 in., and BC =
12 in. for a time of 1/40 or 0.025 of a second. Supposing now a flat plate,
BC = 12 in. wide move from DA to CB during 0.025 second, it will be readily
seen that a drop of water starting from A will have arrived at C in 0.025
second, having been flowing along the surface BC from B to C without either
friction or loss of velocity. If now, instead of a straight plate, BC, we
substitute one having a concave surface, such as BK in Fig. 2, it will be
found necessary to move it from A to L in 0.025 second, in order to allow a
stream to arrive at C, that is K, without, in transit, friction or loss of
velocity. This concave surface may represent one bucket of a turbine.
Supposing now a resistance to be applied to that