A Treatise On The Principles And Practice Of Dock Engineering
Forfatter: Brysson Cunningham
År: 1904
Forlag: Charles Griffin & Company
Sted: London
Sider: 784
UDK: Vandbygningssamlingen 340.18
With 34 Folding-Plates and 468 Illustrations in the Text
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VELOCITY OF EFFLUX FROM SLUICES. 241
and in rectangular culverts,
Ir.-TJO.1M + 3-104 (£)!],
are formulæ enunciated by Weisbach, r being the radius of curvature of
the centre line, and O the angle through which the culvert is bent For
very sharp turns, or knees,
F4 = 0-946 sin2 ~ + 2'05 sin4~.
The head necessary to overcome all these varied sources of friction must
be deducted from the total head, and the residue will then represent the
head available for producing velocity of exit, in accordance with the
formula
v2 = ^^H.
The theoretical quantity of water discharged is
Q = Au,
where A is the area of opening, but in practice it is further necessary to
take into account a modification due to the contraction of the free effluent
leaving the culvert, by which the effective area of the current is less than
the total area in a certain ratio, dependent on the shape of the outlet.
This is brought about by the convergence of the particles into a vena con-
tracta, or contracted vein.
Calling the pipe or culvert area unity, the following are coefficients (c)
of actual discharge in the formula Q=cAu.
For wide openings, whose bottom is on a level with
that of the reservoir; for culverts with walls in a
line with the orifice, ...... -96.
For narrow openings, whose bottom is on a level with
that of the reservoir, ...... -86.
For sluices, without culverts or side walls, . . . -61.
In the foregoing investigation we have only credited the fluid current
with the energy due to motion and to head or pressure, this being the case
when the culvert is truly horizontal. When, however, there is a fall or
inclination in the culvert the water possesses another source of energy,
viz., energy of position, and this leads us to undertake an investigation into
the principles which govern the flow of water in inclined pipes and culverts.
Reverting to the laws of fluid friction stated on p. 239, and remem-
bering thatwhen motion has become uniform, the acceleration and retardation
of a current neutralise each other, we can form the following equation
connecting the two. The acceleration is that due to the action of gravity
on a body falling down an inclined plane of height, h, and length, I. Accord-
ingly,
ff ^— X constant;
16