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 1J 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. s 
If H 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 : 
H=g+H +H 1 +H 2 +H 3 +H 4 
In the above equation V is the velocity at which the water leaves 
the tube ; H is the loss of head at entrance ; H ± the loss due to fric- 
tion; H 2 the loss due to enlargement of section; II 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 
