191. Change of Hydraulic Gradient by Changing Diameter of Pipe.—It has already been seen, in the case of closed pipes or conduits, that the hydraulic gradient with slope s governs the velocity of flow, and also that all parts of the pipe-line must be kept below that gradient. It is sometimes desirable, in order to meet conditions either of topography or of flow, to raise or lower the hydraulic gradient over the whole or some portion of the pipe-line. This can easily be done to any needed extent by varying the diameter of the pipe. An increase in diameter will in general decrease the velocity of the water and increase its pressure, thus increasing correspondingly the height of the columns of water in the piezometer tubes. As the top surface of the latter determines the hydraulic gradient, it is seen that increasing the diameter of a portion of the pipe-line will correspondingly raise the gradient over the same portion. Thus by a proper relative variation of diameters the hydraulic gradient of a given pipe-line may readily be controlled within sufficient limits to meet any ordinary requirements of this character.

192. Control of Flow by Gates at Upper End of Pipe-line.—Obviously, if the pressure in the pipe-line is diminished, less thickness of metal will be required to resist it, and a corresponding degree of economy may be reached by a decrease in the quantity of metal. In the 21 miles of 48-inch steel-plate pipe of the East Jersey Water Company there is a fall of 340 feet; if, therefore, the flow through that pipe were regulated by a gate or gates at its lower end, the lower portion of the line would be subjected to great intensity of pressure. If, however, the flow through the pipe is controlled by a gate or gates at its upper end, enough water only may be admitted to enable it to flow full with the velocity due to the hydraulic gradient. By such a procedure the pressure upon the pipe over and above that which is necessary to produce the gradient is avoided. This condition is not only judicious in the reduction of the amount of metal required, but also in reducing both the leakage and the tendency to further leakage, which is largely increased by high pressures. This feature of control of pressure in a long pipe-line with considerable fall is always worthy of most careful consideration.

193. Flow in Old and New Cast-iron Pipes—Tubercles.—The velocity of flow through cast-iron mains or conduits or through the cast-iron pipes of a distribution system of public water-supply depends largely upon the condition of the interior surface of the pipes as affected by age. All cast-iron pipes before being shipped from the foundry where they are manufactured are immersed in a hot bath of suitable coal-tar pitch composition in order to protect them from corrosion. After having been in use a few years this coating on the interior of the pipes is worn off in spots and corrosion at once begins. The iron oxide produced under these circumstances forms projections, or tubercles as they are called, of greatly exaggerated volume and out of all proportion to the actual weight of oxide of iron. When the pipes are emptied these tubercles are readily removed by scraping, but before their removal they greatly obstruct the flow of water through the pipes. Indeed this obstruction is so great that the discharging capacity of cast-iron mains must be treated in view of its depreciation from this source.

Table XVII exhibits the value of the coefficient c to be used in Chezy’s formula for all cast-iron pipes having been in use for the periods shown.

TABLE XVII.

TABLE OF VALUES OF f AND c.

• LEGEND:
• (A) = Diameter, Inches.
• (B) = Hydraulic Radius r, Inches.
• (C) = Velocity, Feet per Second.
• (D) = Coefficient c.
• (E) = Coefficient f.

Obviously it is not possible to clean the smaller pipes of a distribution system, but large cast-iron conduits may be emptied at suitable periods and have their interior surfaces cleaned of tubercles or other accumulations. At the same time, if necessary, a new coal-tar coating can be applied.

Table XVIII exhibits the values of the coefficient c to be used in Chezy’s formula for new and clean coated cast-iron pipes. It represents the results of actual hydraulic experience and is taken from Hamilton Smith’s “Hydraulics.” A comparison between this table and that which precedes will show how serious the effect of tubercles may be on the discharging capacity of a cast-iron pipe.

In using Chezy’s formula, v = c√rs, in connection with either Table XVII or XVIII, the slope or sine of inclination s of the hydraulic gradient may be readily computed by equation (10), which gives the head lost by friction in a closed circular pipe as

It is only necessary in a straight pipe or one nearly straight to compute the quantity

TABLE XVIII.

VALUES OF c IN FORMULA: v = c√rs.

194. Timber-stave Pipes.—In the western part of the country long conduits or pipe-lines are frequently constructed of timber called redwood. Staves of suitable thickness, sometimes 1¾ inches, are accurately shaped and finished with smooth surfaces so as to form large pipes of any desired diameter. These staves are held rigidly in place with steel bands drawn tight with nuts on screw ends, so as to close tightly the joints between them. Such wooden conduits are rapidly and cheaply built and are very durable. They have the further advantage of requiring no interior coating, as the timber surface remains indefinitely unaffected by the water flowing over it. The latter part of Table XV shows coefficients for Chezy’s formula which may be used for such a class of timber conduits. As the interior surfaces of such closed conduits are always very smooth, the coefficients are seen to be relatively large, and such pipes are, therefore, well adapted to maintain unimpaired discharging capacity for great lengths of time.