MOVABLE DAMS. 213 



The sill of the weir is usually placed higher than that of the pass and its elevation 

 depends on its relation to the length of spillway, as shown in the next paragraph. 

 Where several weirs are employed on the same dam, their sills usually conform approxi- 

 mately to the natural bed of the river. 



Length of Pass and Weir. In determining the lengths required, the chief con- 

 ditions to be satisfied are that the pass shall be long enough to permit ample room for 

 tows going through, and that this length, combined with the elevation of the sill, shall 

 be such that there will be only a very slight fall or "swell-head" there when the navi- 

 gable depth on it is at a minimum. The last condition is an important one, as, if there 

 is a fall of more than a few inches the current will prove too strong for ascending boats. 



To illustrate the methods used in solving the problem an example from actual 

 practice is given. In this case the pass was assumed as 130 feet long and the "swell- 

 head" was assumed as 0.5 foot. The lock, which was assumed to be opened during 

 floods, thus assisting in the discharge, was 52 feet wide. After construction the swell- 

 head was found to be about 0.4 foot, the lock gates being kept closed except when 

 deposit had to be washed out of the chamber. 



The following calculations were made to determine the principal dimensions : * 



"Assuming a value of 0.5 foot for the swell-head, the question then is to deter- 

 mine the maximum stage of the river, the discharge corresponding to which will pass 

 through the pass and lock without causing an increase in depth of water above the dam 

 over that below the dam exceeding 0.5 foot. This will give the elevation of the sill of 

 the weir above the sill of the pass. 



"To determine this the Chanoine formula is used, to wit: 



Q = M(LH + L'H') V2g(Z + h), 



in which Q = discharge of river in cubic feet per second ; 

 M = constant depending on stage ; 

 L = length of pass in feet; 

 L' length of weir in feet; 



H = height of water below dam above sill of pass = stage in this case ; 

 H' = height of water below dam above sill of weir ; 

 v = observed velocity of approach ; 



v 3 

 h = height due to observed velocity of approach = ! 



g = 32.2 feet; 



Z = swell-head, as explained above. 



"For any stage H the discharge through the pass will be Q' =M (i^oH) Vsg(Z + h), 

 and through the lock Q" = M[$2(H - 1.25)] \ / 2g(Z + h), as the upper miter-sill 

 is 1.25 feet higher than the sill of the pass; so that for the pass and lock Q = Q' + Q" = 

 M(iS2H-6$) V2g(Z + h). For H = 5 feet, M = .703, v = 2.72 feet, and the equa- 



* Annual Report Chief of Engineers, U. S. A., 1897, p. 2538. 



