But, it will be urged, it is just the same thing to drive a large body
of water astern at a slow speed as a small body at a high speed. This
is the favorite fallacy of the advocates of hydraulic propulsion. The
turbine or centrifugal pump put into the ship drives astern through
the nozzles at each side a comparatively small body of water at a very
high velocity. In some early experiments we believe that a velocity of
88 ft. per second, or 60 miles an hour, was maintained. A screw
propeller operating with an enormously larger blade area than any pump
can have, drives astern at very slow speed a vast weight of water at
every revolution; therefore, unless it can be shown that the result is
the same whether we use high speed and small quantities or low speed
and large quantities, the case of the hydraulic propeller is hopeless.
But this cannot be done. It is a fact, on the contrary, that the work
wasted on the water increases in a very rapid ratio with its speed.
The work stored up in the moving water is expressed in foot pounds by
the formula

W v² / 2g

where W stands for the weight of the water, and v for its velocity.
But the work stored in the water must have been derived from the
engine; consequently the waste of engine power augments, not in the
ratio of the speed of the water, but in the ratio of the square of its
speed. Thus if a screw sends 100 tons of water astern at a speed of 10
ft. per second per second, the work wasted will be 156 foot tons per
second in round numbers. If a hydraulic propeller sent 10 tons astern
at 100 ft. per second per second, the work done on it would be 1,562
foot tons per second, or ten times as much. But the reaction effort,
or thrust on the ship, would be the same in both cases. The waste of
energy would, under such circumstances, be ten times as great with the