RIVER AND INLAND NAVIGATION.
.251
Whatever system he adopted for such river-works, it is indispensably necessarythat any defect be remedied at once. Constant inspection, great care, and continuallabour, are the only means by which the banks of rivers can be maintained. Noshort-sighted notions of economy should be allowed to interfere with the organizationof an efficient system of maintenance.
50. When rivers bring down small volumes of water, the simplest method of ren-dering them navigable is by the erection of dams or barrages across their beds, thuscreating a series of ponds. The communication between these ponds may be effectedby sluices, as before observed in the case of floatable rivers, or by locks, or eventhrough a pass left constantly open. These last are, however, simply transversejetties, which narrow the bed of the river.
Dams may be either fixed in their whole height, or they may he moveable in such
a manner as to leave a free passage for the waters in time of floods.
Formulae of Flow The object of continuous dams is to cause the waters to rise on their up-side, so asof Water.
to obtain a sufficient depth for the purposes of the navigation. Their result is todiminish the depth of the waters below, in consequence of the additional velocityacquired by the fall over the crown of the dam. The depth of water upon the crowndepends upon the length of the dam. M. CasteTs formula for ascertaining it (whichis generally adopted by Engineers in calculations of this nature) is
x = 0-64 V
in which x is the height sought; Q, the discharge per second; and L, the length ofthe dike or bank.
51. Although the dam produces the effect of retarding or heaping up the waters,it is not immediately upon it that they attain the greatest depth, but at a certaindistance above. The surface of the fluid assumes a convex form before arriving atthe dam, the curve of which commences at a very considerable distance. MM.Guilhem and D’Aubuisson consider the curve to be a portion of a hyperbola whosesummit is above the dam before the waters begin to fall, and whose asymptote is theline of the natural mean fall of the waters before the establishment of the dam. Theequation of this curve would be
( y + p x\ 3 p x 1
H/ ~ IT - I + 4 H {pxf9 H ’
in which x is the horizontal distance of any point in the curve to the dam ; y is theheight to which the waters are heaped up at that point above the original level;II, the greatest height to which they are raised; p, the fall of the bed of the river, inthis case supposed to be straight.
It is usual to place the dams at sufficient distances from one another to allow thelevel of the waters thus kept back to meet the level resulting from the natural fall ofthe bed. The crown is kept at about from 8 inches to 1 foot below the height calcu-lated for the augmented depth. The formula for calculating more exactly the dis-tance of the extreme point of the difference of level created by the dam is (supposingthe coefficient of contraction to be 070)
q = 1 -UldV d+ 0-08
in which q is the quantity of water discharged per second; l, the width of the dam;