If a short pipe bent at right angles like the letter =L= is fitted by
one arm on to the end of the tap, while the other is turned vertically
upwards, and the vat is full as before; when the tap is turned, the
water will shoot up into the air, and after rising for a certain
distance will stop, and then fall. In fact we shall have a fountain.
Observe the difference between the vertical jet of water and the
horizontal jet. If we leave the resistance of the air out of
consideration, the water in the horizontal jet has no obstacle to
overcome; and it might go on for ever, if its weight did not gradually
cause its path to become more and more bent towards the earth, against
which it eventually strikes.
When the jet is vertical the case is altered. The water thrown up
vertically constantly tends to fall down vertically, as any other heavy
body would do, and its momentum has to overcome the obstacle of its
gravity. Any given portion of the water is, in fact, acted upon by two
opposite tendencies, momentum urging it up, and gravity pulling it down.
Now if two equal tendencies exactly oppose one another, the body upon
which they act does not move at all; while, if one is stronger than the
other, the body moves in the direction of the stronger.
Thus a portion of water which has just left the spout shoots up, because
the velocity with which it is impelled upwards is sufficient to carry it
through a greater space in a given time, say a second, than that through
which its gravity would, in the same time, impel it downwards.
But the distance which the water will travel during this second will be
the difference between the distance which it would have ascended if
there had been no gravity forcing it down, and the distance which it
would have descended if there had been no momentum driving it up; and,
at the end of the second, the rate of its motion upwards, or its
velocity, will be proportionally slower. Thus, at the end of the first
second, the water has spent a certain portion of its momentum in
overcoming its gravity. And as there is nothing to make good the loss,
it would, if left to itself, travel more slowly, or over a less
distance, in the second second than it tended to do in the first. But
though the momentum of the water is diminished, its gravity, weight, or
tendency to fall downwards, for a given distance in a second, remains
exactly what it was, and operates in the course of the second second to
exactly the same extent as in the first. Hence, at the end of the second
second, the distance through which the water travels upwards is still
smaller, and its velocity is still more diminished. It is obvious that,
however great the disproportion between momentum and gravity to start
with, gravity must gain the day in the long run under these
circumstances. The store of momentum will be used up; and, after a
momentary rest, the water, reduced to the condition of a body without
support, will begin to be carried downwards by the unopposed action of
gravity.
The case is similar to that of a boy sculling a boat, the bows of which
are suddenly seized and the boat thrust violently backwards by a strong
man. The boat will go stern-foremost rapidly, at first, but every stroke
of the boy’s oar at the stern will retard its backward motion; until, at
length, the stock of momentum conferred upon it by the man’s thrust will
be completely exhausted in working against the boy, and the boat, after
a momentary rest, will resume its onward course. The distance to which
the boat will be propelled backwards will evidently depend upon the
amount of muscular power which the man, as it were, suddenly capitalizes
in the boat, and which the boat then slowly pays out.
We call people who possess much muscular or other power energetic; and
we estimate their =energy= by the obstacles they overcome, or, in other
words, by the =work= they do. In the present illustration the man’s
energy would be measured by the distance to which the boat was propelled
before it stopped.
It is easy to transfer this conception of energy, as the power of doing
work, to inanimate things; and thus when a body in motion overcomes any
kind of obstacles in its way, parting with its momentum and more or less
coming to rest in the process, we say that it has =energy= and that it
does =work=.
The energy of moving water is thus measured by the intensity of the
opposing forces which it can overcome multiplied into the distance which
it can travel before that energy is exhausted; that is to say, by the
work it does before it is itself reduced to a state of rest. In the case
under consideration, the energy by which gravity is overcome, for a
greater or less time, depends upon the velocity of the stream; and this
again depends upon the height of the water in the vat above the tap.
Just as the energy of the horizontal stream diminished as the level of
the water became lower, so does the energy of the vertical stream
diminish. Hence, as the vat empties, the jet becomes shorter and
shorter, until at last it sinks down to nothing.
The energy of moving water makes it, under some circumstances, one of
the most destructive of natural agents; and, under others, one of the
most useful servants of man. A stream is water falling down hill with a
velocity depending upon the inclination of its bed. As it falls it
acquires momentum and, hence, energy; and thus a mountain stream,
suddenly swollen by rain or melting snow, will tear away masses of rock
and sweep everything before it. Nothing can look softer or more harmless
than a calm sea, but if the wind sweeping over its surface puts the
water in motion, it strikes upon the shore with terrific force; and its
energy is expended in throwing up great waves, which lift vast blocks or
drive masses of shingle up the beach.
In all kinds of watermills it is the energy of more or less rapidly
falling water which is turned to account. The water is made to flow
against buckets or floats attached to the circumference of a wheel. Each
bucket or float is therefore an obstacle to which the water transfers
some of its own motion; it moves away and thus makes the wheel to which
it is fastened turn. But the turning of the wheel brings a new obstacle
in the way of the stream. This is treated in the same fashion, and the
wheel turns still further, thus introducing another obstacle in the way
of the stream upon which the same effect is produced. Thus each float,
or bucket, is a means by which some of the momentum of the stream is, as
it were, caught and transferred to the water-wheel, which consequently
turns round with a certain velocity.
But this water-wheel is now a mass of matter in motion, and therefore
itself contains a store of energy or power doing work. If a cord with a
weight at the end of it were fastened to the axle of the wheel, the cord
would be wound upon the axle, and the weight could be raised, or, in
other words, so much work would be done by the turning of the wheel and
we should thus have a rough measure of the amount of energy which had
been given up by the stream to the wheel.
The machinery of the mill is simply a set of contrivances for
transferring the energy stored up in the water-wheel to the place in
which work has to be done. In a flour-mill, for example, a series of
wheels carries it from the water-wheel to the grindstones, which it sets
in motion.