Ancient and Modern Engineering and the Isthmian Canal

Table XIV

LEGEND:

(A) = Depth, in Feet.

(B) = Hydraulic Radius r, Feet.

(C) = Coefficient c.

(D) = Mean Velocity, Feet.

(E) = Cubic Feet per Second.

(F) = Gallons per 24 Hours.

Aqueducts.	(A)	(B)	Grade s.	(C)	(D)	Discharge.		n in Kutter’s Formula.
						(E)	(F)
† New Croton (1899)	8.42	3.974	.0001326	153.3	3.52	371.6	240,200,000
† ”” (after two years’ use)	..	2.338	″	131.3	2.312	..	..	.0133
‡ ””	..	1	″	119.3	1.374
‡ ””	..	1.5	″	126.3	1.781
‡ ””	..	2	″	129.8	2.114
‡ ””	..	2.5	″	132	2.404
‡ ””	..	3	″	133.4	2.661
‡ ””	..	3.5	″	134	2.887
‡ ””	..	4	″	134.4	3.095
Old Croton (1899) clean	6	2.338	..	133.4	2.958	122.8	79,400,000	.0133
”” ordinary condition;	6	2.338	..	123.2	..	..	73,300,000
not clean
”” not clean	7.33	2.368	..	118.2	..	..	85,600,000
Dorchester Bay tunnel	..	1.875	..	119
””	..	2.338	..	125.0	..	..	..	.014
Wachusetts, new; probably	..	..	..	144.9
clean (approx.)
Sudbury, clean	..	.5	.000189	116.9	1.14
””	..	1.0	″	127.0	1.74
””	..	1.5	″	133.3	2.24
””	..	2.0	″	137.8	2.68
””	..	2.5	″	140.4	3.04
† From report by J. R. Freeman to B. S. Coler, 1899.
‡ From report of New York Aqueduct Commission.

190. Flow of Water through Large Closed Pipes.—The masonry conduits to which consideration has been given in the preceding paragraphs carry water precisely as in an open canal, but the closed conduits or pipes of steel plates and cast-iron, like the Hemlock Lake conduit at Rochester and the East Jersey conduit of the Newark Water-works, are of an entirely different type, as they carry water under pressure. Hence the slope or sine of inclination s belongs to the hydraulic gradient rather than to the grade of the pipe itself. Where the pipe-line is a long one its average grade frequently does not differ much from the hydraulic gradient, but the latter quantity must always be used. As in the case of the masonry conduits, the coefficient c in Chezy’s formula will vary considerably with the degree of roughness of the interior surface of the pipe, with the slope s, and with the mean radius r. An important distinction must be made between riveted steel pipes and those of cast-iron, for the reason that the rivet-heads on the inside of the former exert an appreciable influence upon the coefficient c. The rivet-heads add to the roughness or unevenness of the interior of the pipe. Table XV gives the elements of the flow or discharge in the two pipe-lines which have been taken as types, as determined by actual measurements; it also exhibits similar elements for timber-stave pipes, to which reference will be made later.

As would be expected, the velocity of flow in these pipes may be and generally is considerably higher than the velocity of movement in masonry channels. Both Tables XV and XVI give considerable range of coefficients computed and arranged from authoritative sources, and the coefficients c for Chezy’s formula represent the best hydraulic practice in connection with such works at the present time. In using the formula for any special case, great care must be taken to select a value for c which has been established for conditions as closely as possible to those in question. This is essential in order that the results of estimated discharges may not be disappointing, as they sometimes have been where that condition so necessary to accuracy has not been fulfilled.