242
DOCK ENGINEERING.
or, substituting S for y, the sine of slope, and introducing instead of»
1 Ra
so as to express the equation in terms of the hydraulic mean radius, we have
V2
yS = — x constant,
R
which reduces to the form
V = Ox/RS, ............................(40)
and this constitutes the basis of a very large number of expressions for the
velocity, the values for C ranging from 70 to 100, according to the personal
observation of different experimentalists.
Kutter’s value for C, though complex, is recognised as the most generally
reliable, and it is here given
0 =
41-6 +
1811
a
•00282
S
-00282\
‘H*-r)
(41)
a
in which a has the following numerical équivalents : —
• 009 for well-planed timber channel.
• 010 „ cement plaster channel.
• 011 ,, cement and sand plaster channel.
• 012 „ common boards, unplaned.
• 013 „ ashlar and neatly-jointed brickwork.
• 017 „ rubble masonry.
• 025 ,, earth surface.
• 03 ,, detritus and uneven ground.
Strictly speaking, the amount of head introduced into the foregoing
equation should be the total head reduced by that portion required to over-
come the friction of entrance into the culvert, but when this latter is very
small in comparison with the former, as it is in long conduits with moderate
heads, the total head may be used without sensible error.
For the sake of example let us take the case of a horizontal culvert,
6 feet high by 4 feet wide, and find the amount of head required to produce
an exit velocity of 4 feet per second. Assume a length of 100 feet, a square-
edged entrance, and one bend of 60° in direction, with a radius of 5 feet.
Then, by the preceding formulæ,
f! =/^ . . . = .625
F2 ........................= -505
r,-^{om+ s««^)*}
- J{0124 + 3104 (^)4} . . - .0«
F = FT + F2 + F3 = 1-175