5^
DOCK ENGINEERING.
If the gate chain be attached at a distance, x, from the same origin, the
.équivalent mass on the line of pull is
M x -577
= m, say.
X
Now, if it be desired to impart to such a mass a velocity of v feet per
V
second in, say, t seconds, the acceleration will be -, and the force,/, required
to produce it
m V
- x -.
U 1
(136)
The second force, /2, which is required to overcome friction, may be
estimated with the aid of a suitable coefficient, c, at some fraction of the
weight (W) to be moved.
/2=cW............................(137)
Lastly, the resistance of the water to displacement during movement is
theoretically determined by the considération that the pressure on the plane
of the gate is some factor of the pressure which would be produced by a
body of water falling upon the gate with a velocity equal to the velocity of
movement of the latter.
If h be the distance through which the water is supposed to fall, we
have, in Ibs.,
= A. . wh. k
. (138)
where, for fresh water, w = 621 Ibs. and A = 1-8 ; and for salt water,
w = 64 Ibs. and k = 1’85. A is, of course, the area in feet of one surface of
the leaf.
As an example let us take the case of a greenheart gate, 55 feet long by
40 feet deep, with the possibility of the full extent of head, and suppose it
to be worked by a chain attached at a point 10 feet from the outer extremity
of the leaf. Assume the weight of the gate to be 150 tons. Then
150 x -577 x 55
m = -------------------= 105-8 tons ;
45
and if it be deemed desirable to obtain a speed of 1 foot per second, in ten
seconds,
- 105-8 .
/= x ^ = -33 ton.
This is on the supposition that the pull is horizontal; any deviation
therefrom would necessitate a suitable modification.
The frictional coefficient is most difficult to estimate in the case of a dock
gate, there being so many modifying influences at work. For a railway
train travelling at normal speed about 10 Ibs. per ton would be considered a
fair allowance, but this coefficient is manifestly too low for a cumbersome