ai4 THE IMPROVEMENT OF RIVERS. 



Hon becomes O - .703 X 845 X 8.02 X .784 - 3735 cubic feet, which is considerably 

 greater than the discharge corresponding to a s-foot stage. Making // in the formula 

 equal to 6 feet, M becomes equal to .71, v - 2.99 feet, and there results Q = .71 X 

 1027 X 8.02 X .8 4678, for the discharge by the lock and pass with a swell-head of 

 0.5 foot. If Z is taken as equal to 0.5 foot, and the sill of the weir is made 6 

 feet above that of the pass, // becomes 0.5 foot, anil M is reduced accordingly. 

 Taking L' equal to 140 feet, the discharge over the weir becomes equal to 180 cubic feet 

 per second, so that the quantity of water that can pass the dam per second, the lock 

 gates being open, without producing a greater swell-head than 0.5 foot, is 4858 cubic 

 feet. The discharge of the river corresponding to a 6-foot stage is 4910 cubic feet per 

 second, so that the swell-head corresponding to this discharge would be but little in 

 excess of 0.5 foot. 



"In determining the length of the weir the following conditions must be satisfied: 

 i st. The area of discharge afforded by the weir must be sufficient, when taken in con- 

 nection with those of the pass and lock, to permit the passage of discharges correspond- 

 ing to all stages up to the level of the top of pier and abutment, without causing a 

 greater swell-head than 0.5 foot. 2d. The discharge area of the weir should be suffi- 

 cient to pass all discharges corresponding to stages up to that at which the natural river 

 is navigable, without the removal of any needles from the pass. It may be stated, 

 however, that the second condition will be satisfied by a length of weir that will satisfy 

 the first. 



"To determine the length of the weir, the elevation of its sill being fixed, the formula 

 of Chanoine, modified to take into account the discharge through the lock, is used, to wit : 



"Q -- M[LH + $2(H 1.25) + L'H'] Vag(Z + h), or substituting for L its 

 value already determined, 130 feet, the formula becomes Q = AI(i&2H 65 + L'H') 

 \/2g(Z + h) ; making H equal to 7 feet, H' becomes equal to i foot, and the formula 

 becomes Q = M (1209 + L') \/2g(Z + /t). For a stage of 7 feet, 0=6362 cubic 



feet, M = .73, h = = .160 and (Z -f h) H = .812, whence L' becomes 



equal to 129.3 



"For high stages, the formula of Chanoine and De Lagren is used, to wit: Z = 



(S 2 \ i 

 -~, i ) , in which Z = swell-head, V = mean velocity before construction of 



works, S = discharge area of river before construction of works, S' = discharge area 

 after construction of works = LH + L'H', and 1.5 is a constant for cases where the 

 lock gates are open. Transforming the above equation and substituting for 2g and 



/ i sV^S 1 \X 

 Z their values 64.3 and .5, respectively, there results S' = ( - ^- - ^-J . For 



the highest stage observed H = 15.45 feet, H' = 9.45 feet, V = 4.7 feet, and S 4576 

 square feet, and 5' LH + L'H' = 3260 square feet, = 2008.5 square feet + 9.45!^ 

 whence L' - 132.4 feet. 



