SPILLWAYS FOR RESERVOIRS AND CANALS. 5 



other words, if a dam were 30 feet higher than the surface of the 

 tail water at its base, and there were 5 feet of water pouring over 

 its crest, of the 35 feet available head only 5 feet, or about 14 per 

 cent, would be utilized to produce velocity. Since the two principal 

 factors determining capacity are length of crest and head and the 

 allowable increase in head is small, the only available means for 

 increasing discharge is by increasing the length. One of these 

 factors directly governs the other and only by knowing one of them 

 definitely can the other be determined; or if the discharge of the 

 stream is known and the head allowable as a depth of overflow is 

 definitely fixed, the length of spillway to provide a specified dis- 

 charge can be computed from the standard wier formulas by select- 

 ing the proper coefficient for the form of weir crest under considera- 

 tion. These formulas and their corresponding coefficients are very 

 indefinite because of the fact that they have never been proven to be 

 accurate for heads of more than 4 or 5 feet over the crest of the 

 weir. 



Furthermore, in determining the required capacity of the spill- 

 way, a careful study must be made of the record or data relating 

 to the precipitation or run-off of the catchment basin it is destined 

 to serve and a liberal factor of safety added to the results of the 

 computations to insure security in case of discharge greatly in 

 excess of any known flood record, and in spite of the retentive 

 capacity of the reservoir. 



Long crests discharging thin sheets of water will give greater 

 factors of safety than short spillways with greater depths, will 

 afford less liability to fracture or do other damage to the dam as a 

 result of the impact of the heavier volume of water, and will insure 

 closer regulation of the pond level. 



In the common formulas applied to determine spillway capacity, 

 there are different elements to be considered in their application 

 to the case under consideration, such as height of crest above the 

 bed of the reservoir or canal upstream from the crest, length and 

 width of crest, velocity of approach, correct determination of the 

 head on the crest, and the number of end contractions, if any. All 

 these influence the efficiency of the structure as a whole. 



Possibly the formula most used in the United States is the Francis 

 formula expressed in its simplest form as Q = CLHi^, and which is 

 modified by the introduction of the elements referred to above where- 

 ever they apply. For instance, with velocity of approach this for- 

 mula would be changed to read 



Q = CL[(H + h)!-hfl 

 and if it considers velocity of approach and end contractions it must 

 still be modified to read 



Q = C(L-0.2H) [(H-fh)t-hl]. 



