Regarding the upward pressure on the floor due to the hydrostatic pressure from the head A B, there is a theory that the weight of a portion of the floor at any point P should be able to balance the pressure due to a head of water P R. This, supposing the masonry to be twice as heavy as water, would give a thickness of floor equal to half P R. According to Bligh, the theoretical thickness ought, for safety, to be increased by one-third. Practically the thickness need not, in most cases, be made even so great as is given by the theoretical rule. On canals in the Punjab it is certainly less. Water passing through soil or fine sand does not exert anything like the pressure which it exerts when passing through a pipe. It acts in the same manner as in a capillary tube. It is only in coarse sand or gravel or boulders that water flows as in a pipe.[12] If the tail water covers the floor, the weight of a portion of floor is reduced by the weight of an equal volume of water. If the foundation of any part of the floor is higher than B E, the upward pressure on it is reduced because the water has to force its way upwards through the soil.
Bligh also states as an empirical rule that in order to provide efficiently against scour the length of floor B E should be 4/s √(H/13), where H is the maximum head A B; and he points out that in a case where this length is less—as it usually is—than that necessary to give a hydraulic gradient of the requisite flatness, according to the rule previously quoted, it is better to add an upstream floor B D, which may be of puddle and therefore cheap, than to add to the downstream floor a length E C which must be of masonry or concrete, and that this arrangement, by shifting the line of hydraulic gradient from A E to F E, gives a reduced upward pressure on the downstream floor.
The length E N to which pitching, if of “rip-rap” type, should extend is given by Bligh as 10/s √(H/10) √(q/75), where q is the maximum discharge in cubic feet per second passing over a 1-foot length of the weir, and H is the head A B.
4. Various Types of Weirs.—The type of weir shown in [fig. 32] may be varied by steepening or flattening the slopes of one or both faces. Flattening increases the cost but gives a greater spread for the foundations. It may, however, be combined with a decrease in the width of the crest. Flattening of the downstream slope reduces the shock of the water on the floor, but the slope itself, especially the lower portion, has to stand a good deal of wear, and the length exposed to this is increased. Flattening the upstream slope facilitates the passage of floods. The same result is obtained by making the crest slope upwards ([fig. 34]). In a small stream or in an irrigation distributing channel, a weir may be a simple brick wall with both faces vertical and corners rounded.
Fig. 34.
Weirs in America are often built of crib-work filled with stones. Weirs are also made of sheet piling filled in with rubble, and the top may be protected by sheet iron. A weir made on the Mersey in connection with the Manchester Ship Canal works was so made. There were three rows of piles and the filling in the back part was of clay.
Sometimes the downstream faces of weirs used to be made curved ([figs. 35] and [36]), the object being to reduce the shock of the falling water, but the advantage gained is not very appreciable, and this type of weir is not very common.
Fig. 35.