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 = CLH/2 , 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)f-hf] 
and if it considers velocity of approach and end contractions it must 
still be modified to read 
Q = C(L^-0.2H) [(H+h)f-hf]. 
