H==^+H +H 1 +H a +H,+H 4 



SPILLWAYS FOR RESERVOIRS AND CANALS. 23 



velocity as induced by a perfect vacuum. On one such installation 

 known to the writer, where the most minute study was given to the 

 computations for the design of the different parts of the siphon, and 

 the maximum available head for producing velocity was 11.87 feet, 

 the mercury gage used on a test of the structure indicated a partial 

 vacuum equivalent to 15.60 feet. This was noted as suggesting that 

 the siphon was acting in a manner similar to a compound diverging 

 tube under pressure, and yielding a coefficient of discharge greater 

 than 1 and which may even have approached 1| or 2. 



As stated above, in a discussion of the computations for the proper 

 proportioning of the parts, one may go thoroughly into the theo- 

 retical determination of their dimensions, but must come back to the 

 realization that the data are too meager to justify any conclusions 

 and surrender to the simpler formula based on the elements of cross 

 section, velocity, and a predetermined constant. 



If II represent the effective head — that is, the difference in eleva- 

 tion between the water surface at the inlet of the siphon and the sur- 

 face in the tail water or the mid point of the outlet end (depending 

 upon whether or not the outlet is submerged) — we may express the 

 losses due to all causes in the passage of the water through the siphon 

 as follows : 



Yl 



m V 



In the above equation V is the velocity at which the water leaves 

 the tube ; H is the loss of head at entrance ; I\ the loss due to fric- 

 tion ; II 2 the loss due to enlargement of section ; H 3 the loss due to 

 contraction ; and H 4 the loss of head due to bends. 



Velocity of approach has the same influence on a siphon spillway 

 as on a crest spillway, but this influence is so small compared to the 

 influence of the head of elevation that it can be ignored. 



Because of the fact that the outlet basin of most siphons is so con- 

 structed that the velocity head is completely dissipated in eddies, no 

 mention is made of any recovery of velocity head. This formula, 

 therefore, accounts for the elements which hydraulicians agree con- 

 tribute to form a factor of efficiency for the structure as a whole. 



No tests on other than laboratory models have been conducted to 

 obtain correct results of the actual application of the factors, or to 

 what extent they are influential. 



It is assumed that an ideal inlet will be largely flared and then 

 taper to the smallest cross section of the siphon, which is usually 

 at the throat, because it is known that from tests on pipes of small 

 cross section and of different materials the entry loss for a bell- 

 mouthed intake will approach a value of 0.05H V . The value 0.25H V 

 has been assumed as the extreme limit for loss from shock or bend, 

 but this has not been proven, in pipes of large diameter. Whether 

 or not the assumption is correct can not be stated, and is here taken 

 to apply where the radius of curvature is at least equal to the 



