The mean velocity must not be too quick, and should be so determined as to suit the tenacity and resistance of the channel, otherwise the bed and banks will change continually, unless artificially protected; it should not exceed d'Hydraulique, p. 135. When the fall does not exceed a few inches per mile, the velocity, as determined from the inclination, is very uncertain, and for this reason it is always prudent to increase the depths and sectional areas of channels in flat lands, as far as the regimen will permit. In such cases the section of the channel should approximate towards the best form. See pp. 192 and 255. TABLE OF VELOCITIES OF SOME MOVING BODIES COMPARED WITH THOSE OF RIVERS A velocity of 180 feet per minute will remove angular stones the size of an egg. Mr. Phillips, under the Metropolitan Commissioners of Sewers, states that 2 feet per second, or 150 feet per minute, is sufficient to prevent soil depositing in sewers. The fall per mile should decrease as the hydraulic mean depth increases, and both be so proportioned that floods may have sufficient power to carry off the deposits, if any, periodically. The proportion of the width to the depth of the channel should not be derived, for new cuts or river courses, from any formula, but taken from such portions of the old channel as approximate in depth and in the inclination of the surface to that proposed. When the depth is nearly half the width, the formula shows, cæteris paribus, that the discharge will be a maximum; but as (altogether apart from the question of expense) the quantity of water discharged daily, at different seasons, may vary from one to seventy, and more, and "the regimen," has to be maintained, the best proportion between the width and depth of a new cut. should be obtained, as stated, from some selected portion of the old channel, whose general circumstances and surface inclination approximate to those of the one proposed; and the side slopes of the banks must be such as are best suited to the soil. The resistance of the banks to the current being in general less than that of the beds, which get covered with gravel, and the necessary provision required for floods, appears to be the principal reason why rivers are in general so very much wider than about twice the depth, the relation which gives the minimum of friction. The following Table is given by Rennie, as an approximation, generally, to the actual state of rivers.* The surface inclinations, however, given in this table for the first and second classes, are very considerable for large rivers, and would give velocities which would effectually scour them. For a hydraulic mean depth of 12 feet, the velocity, with a fall of 1 12000' would be 2 feet 8 inches per second by Du Buât's formula; and 3.3 feet per second by our formula. The description, therefore, can only apply to smaller channels. In 1 15740' is a considerable in From Carrick-on-Shannon fact, 4 inches to a mile, or clination for a large river. to Killaloe, a distance of 110 miles, the average fall is only about 4 inches per mile on the river Shannon; and the portion between Athlone and the river Suck below Shannon bridge the fall varies from 7 to 13 inch per mile. The Table of the "Falls on the Shannon" (p. 262) explains practically the defects in Rennie's Table, or of any tabular arrangement that omits the size and hydraulic mean depth of the river channel. The mean velocity and quantity flowing remaining the same, the hydraulic mean depth increases as the surface inclination decreases, and in the same ratio. The increase of surface inclination and of velocity are the indices of obstructions in the channel, with this difference, that the obstructions are caused by the velocity where the surface inclination is generally steep; but the obstructions cause the increase of velocity where the inclination is generally flat. |