APPLICATION OF THE LAWS OF HYDRAULICS
VI. RELATION BETWEEN THE HEAD, THE PRESSURE AND THE
VELOCITY OF CURRENTS OF LIQUIDS AND GASES
If the velocity of flow of any current is considered, as in a canal
or a river, it is a function of the head expended. As the bottom
or bed of a torrent of water is never smooth, the velocity of flow
is only maintained by the expenditure of a velocity head sufficient
to compensate for the velocity lost at the obstructions. The
water in a stream flows only when its free upper surface has a
sufficient slope or hydraulic gradient to cover the loss of velocity
due to the friction against the bottom and sides of the stream.
Therefore, there will be no flow or current unless there is a
corresponding loss of velocity head, and if there is a flow there will
be a corresponding loss of velocity head in impressing this velocity
upon the stream and in maintaining it.
If the velocity of the flowing current is v} then
and /& = •«-
in which h represents the velocity head expressed in terms of the
liquid in motion (water, kerosene, liquid iron, mercury, etc.).
For example, when any liquid is impressed with a velocity of
flow of 4 m 43 per second, there will be required, according to
the formula, the expenditure of a velocity head h of 1 m. This
will be 1 meter in height of water, kerosene, liquid iron, mercury,
or of the particular liquid which is in motion.
If this meter of velocity head is expressed in kilograms per
square meter, it will be found that, for each of these different
liquids, a different pressure is required to produce the same
velocity of 4 m 43 per second, according to their density, as follows:
Kilograms per square meter
Millimeters of water
Liquid iron. . . .
Mercury. . . .
1 . 3595