322
DOCK ENGINEERING.
approximate expression for the resultant pressure in terms of the rise and
span of the gates, viz. :—
K-"‘'(is*i)................<“>
The following data apply to a pair of gates closing a 70-foot entrance:—
7=39'75; 8=76-3; r=11 16; />=1; Å=30—all in feet.
By formula (47)
64 x 30 x 30 x 39-75 x 38-75
4 x 11-16
= 1,987,500 Ibs., or 887-3 tons.
By formula (48)
R = 64 x 30 x
76-3 x 76-3 11-16
.16 x 11-16 + 4 .
= 2,038,500 Ibs., or 910 tons.
The discrepancy between the two results, it will be observed, is less than
2| per cent.
Zones of Equal Pressure.—The surface of a gate may be divided into a
series of zones, in which the total hydrostatic pressure is equal, in the
following simple and graphical manner : —
With the height of the gate between the sill and the surface of the water
as diameter, describe a semicircle (fig. 257). Subdivide the diameter into
any number of equal parts (say five) by the points a,b, c, d. Through these
points draw horizontal lines to the semicircle, intersecting it at the points
e,f g, h. Then, with A as centre, describe circular arcs ek, fl, gm, hn,
cutting the gate surface at the points k, l, m, and n. Ek, kl, Im, mn, and
«B will then be a series of consecutive zones upon which the hydrostatic
pressure is in each case equal to one-fifth of the total pressure upon the
surface of the gate.
This may be proved by reference to fig. 258. There it will be seen that
from similar triangles
AO _ AD
AD AB’
AC AD2
or AB - AT32’