GENERAL EXPLANATION 7 
amplitudes of the constituents in an harmonic expression of the current velocity will 
be proportional to the corresponding amplitudes of the tidal constituents multiplied 
by their respective speeds. This becomes evident when the speed of the rise of tide 
is expressed by the first derivative of the formula for the height. Although our assump- 
tion may be only approximately correct, the result suggests that the relative importance 
of the diurnal constituents as compared with the semidiurnal constituents is only about 
one-half as great in the currents as in the tides. For the same reason the relative 
importance of the quarter-diurnal and sixth-diurnal constituents may be expected to 
be greater in the currents than in the tides. 
15. Hydraulic current.—This name is applied to a reversing current in a strait 
when it results from a difference in the tidal head of water at the two ends of the 
passage. The hydraulic current may be considered the indirect result of tidal action 
rather than a direct part of the tide wave. A difference in head may result either 
from a difference in the range of tide at the two entrances to a passage or from a differ- 
ence in phase of the tide, or most generally it results from a combination of range and 
phase differences. Excepting for a lag due to friction and inertia, the hydraulic cur- 
rent would attain its maximum velocity at the time of maximum difference in head, 
and come to a slack when the difference in head is zero. The velocity of the hydraulic 
current should vary as the square root of the difference in head. 
16. Current variations in cross section of a stream.—Currents may be expected to 
vary in respect both to time and to velocity at different points in the cross section of a 
stream. In general, the current near the sides and bottom of a stream turns earlier 
and reaches its maximum strength sooner than it does on the surface in the center of 
the stream. This is due primarily to the friction of the moving water against the sides 
and bottom of the waterway. This friction tends to overcome the inertia of the moving 
water thus advancing the times of occurrence of the different current phases. For the 
same reason the velocity of the current is less near the shores and bottom of a stream 
than it is on the surface in the center. The actual maximum velocity of the current 
is usually found a short distance below the surface because of the friction between the 
water surface and the overlying atmosphere. 
17. The differences in the times and velocities of the current at different points 
in the cross section of a stream will depend largely upon local conditions. The depth 
of water and uniformity of shoreline and bed of stream are important factors and eddies 
may be created by the presence of some nearby obstruction. Differences of a half hour 
or more in the time of the turning of the current near the shore and in midstream are 
quite common. Velocities may vary greatly, but for the purpose of computing stream 
flow through a waterway, it has been roughly estimated that the mean velocity through 
a cross section of a regular channel is approximately three-fourths as great as the central 
surface velocity, this estimate being consistent with observational data obtained in 
some localities. Since the mean velocity for an entire flood or ebb period may be taken 
as approximately 0.637 times the velocity at strength of current (par. 9), it follows that 
the approximate average velocity in the cross section for the tidal period may be ob- 
tained by multiplying the central surface velocity at time of strength by the product 
(0.75 X0.637), or roughly one-half. 
18. A very important factor in the flow of current through a cross section of a 
. Tiver is the fresh water drainage into the stream. This fresh water because of its lesser 
density tends to override the heavier salt water brought in by the tides, especially in 
the lower reaches of the river. Thus, near the surface of the stream there is a more or 
less permanent nontidal flow which increases the velocity of the ebb and diminishes 
