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of 100 gallons per capita, a maximum day of 150 per cent of the average for the year and a peak hour of 150 per cent of the average for the day. Under such conditions, the maximum fire demand based on the Underwriters' formula, coincident with the average rate of consumption of the maximum day, will exceed the "peak hour" rate of ordinary consumption for cities of less than 270,000 population, and will be less than the "peak hour" rate for larger cities.

Local fire demand. Regarding the fire flow which must be available about any one square, this is a matter which for congested high value districts must be decided on the ground. In residential districts, quoting Goldsmith (1924, 12, Amer. Water Works Assn., 168), "sections containing small dwellings of low height occupying not more than one third of the block front require two fire streams, or not less than 500 gallons per minute. Where the buildings are sufficiently close to expose one another, i.e., with a separation of 50 feet or less" four streams should be provided. For higher degrees of development, the Underwriters suggest (Grading Schedule, 1916) "where the district is closely built or buildings approach the dimensions of hotels or high value residences, 1500 to 3000 gallons is required, with up to 6000 gallons in densely built sections of three-story buildings."

In considering the fire flow required for an individual risk, area is the most important element. Next in importance is height, up to a limit of six stories, due to spreading from floor to floor through unprotected vertical openings. Higher buildings nowadays are usually of fire-proof construction, and in any event, must be handled through house-pumps rather than by ordinary methods.

Duration of fire draft. The duration of maximum fire flow for which provision should be made is suggested by Freeman as six hours, and such basis of design is quite common in the smaller cities and towns where dependence for fire supply is placed in part upon storage in standpipes or elevated tanks. The Underwriters recommend five hours fire flow for towns of less than 2500 population, and ten hours for larger communities.

Design for future conditions. It is usual practice to build supply works designed for periods of twenty years or more in the future. This policy is not so closely adhered to in the distribution system because of the uncertainty as to the manner and direction in which

a community will develop, and the desirability-both from the standpoint of safety and of service of conveying the supply into the heart of the town through a number of large mains quite widely separated, instead of concentrating the flow in a single line; such a multiple main layout lends itself well to successive improvements which can be made to keep more closely in step with the current needs. A general plan should, of course, be developed to suit the best estimate of conditions which will obtain twenty or thirty years in the future, and the improvements made from time to time with this in view.

An analysis was made by Hill (1915, Amer. Water Works Assn., 110) of the relative economy of duplicating a pipe of given size in future as opposed to laying a pipe of approximately double the capacity at once, from which the following tabulation is adapted:

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Different market conditions than those assumed by Hill will vary the relation to some extent.

Hydraulic computations

Hazen-Williams formula. In recent years, the "Hazen-Williams" formula for computing the flow of water in pipes has come into increasing favor in water works practice as compared to some of the older forms of expression.

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in which is the velocity of flow in feet per second, C is the coefficient of friction, R is the hydraulic radius of the pipe, and S is the slope of the hydraulic gradient.

Coefficient of friction. The friction coefficient varies widely with

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FLOW OF WATER IN PIPES

Diagram based on the Hazen-Williams Formula, Vicno.6350540.001 -0.04

The diagram shows the number of pipes of a given diameter which will carry the same total quantity of water with the same rate of friction loss as a single larger pipe.

Enter diagram at the bottom with size of single pipe and follow diagonal line to intersection of vertical line indicating size of smaller pipes; read equivalent number of smaller pipes at left of diagram.

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EQUIVALENT NUMBER OF PIPES

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FIG. 6

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NEW CAST IRON PIPE

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the interior condition of the pipe. Its value decreases progressively with age depending upon the character of the water conveyed, in encouragement of tuberculation of the metal and of vegetable growths, and of the deposition of suspended matter in the pipe. New cast iron pipe will usually show a friction coefficient of about 130; hydraulic computations for new work are frequently based upon a value of 100, which under normal conditions represents the condition after fifteen to twenty years of use. In planning the improvement of existing works it is highly important that the values of the friction coefficient of the principal mains of the old system be determined by actual test.

Diagram of flow in pipes. Figure 6 is a logarithmic diagram of the results of the Hazen-Williams formula for the ordinary sizes of pipe with a value of 100 for the friction coefficient C. With other factors constant, the discharge varies directly with the value of C. In the lower right-hand corner of the figure is a small diagram which shows the effect of variation in the value of C upon the loss of head for given rate of flow in terms of percentage of the loss of head for C 100 as shown in the main diagram. The small inset tabulation indicates the age in years at which Hazen and Williams in general found the various sizes of cast iron pipe to have depreciated in carrying capacity to comport with the several values of C, and another minor diagram shows the relative carrying capacities of the different sizes of pipes.

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Compounding system of mains. The process of "compounding" pipes in the hydraulic design of a distribution system has been frequently described, and need not be entered into in detail here. Freeman (1892, 7, N. E. Water Works Assn., 49) favors a graphical solution, plotting head-discharge curves for each route of flow, and compounding by the graphical construction of a curve for which the discharge at any loss of head is equal to the sum of the discharges by the several individual routes. This method has the advantage of all graphical methods in visualizing the relations of the several elements of the problem and tending to avoidance of errors. In case of complications by flow from more than one source, or by variations in the relation of ordinary consumption of fire draft, the use of such curves plotted for at least the principal elements of the system is essential both to grasp and solution of the problem.

It is sometimes desirable to carry the analysis through from source to point of draft by computation, plotting a curve to show the final result. A logarithmic diagram with single line showing on fairly large scale the relative percentage variations between head and discharge according to the Hazen-Williams formula is very useful in such compounding problems and in developing the curve for a system in which the loss of head is known for a single rate of flow. For a small town-up to say 10,000 population-it is a relatively simple matter to develop, by computation, curves which will show quite accurately the fire flow available with varying residual pressures at the several important locations. In such case the piping layout is simple, so that it may be completely compounded with no great labor, and the effect of the coincident ordinary draft is easily allowed for.

Difficulties in the application of theory increase with the size of the system, due to the multiplicity of mains and the complications introduced by distributing the ordinary consumption. The usual problem in a large city is one of reinforcement or extension, and is to be approached only after thorough study of the hydraulic performance of the existing system by means of pressure and flow tests.

General features of design

Three classes of mains. Three classes of distribution mains appear in the make-up of a large system:

1. Primary feeders, constituting the skeleton of large pipes with relatively wide spacing which convey large quantities of water to various points in the system for local distribution through the smaller mains.

2. Secondary feeders, forming the net-work of pipes of intermediate size which reinforce the distributor grid within the various panels of the primary feeder system, and aid in the concentration of the required fire flow at any point.

3. Distributors, consisting of the grid-iron arrangement of small mains serving the individual fire hydrants and blocks of consumers.

Two classes of pressure drop. In such a system, two classes of pressure drop are to be recognized and separately considered:

a. The loss of head in the primary feeder system, varying in general with the total draft.

b. The pressure drop within a relatively small area about the fire, due to concentration of the fire flow.

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