In passing from the pumping station to the regulating reservoir, or I to the point of distribution, the water usually flows through a simple pipe of a uniform sectional area; and, as far as it is possible to secure that condition, with a uniform, constant velocity. In its course, how ever, the water is retarded by a series of resistances, which practically may be resolved into those depending upon :-1. The friction on the sides of the pipes ; 2. The existence of bends, or changes of direction ; and 3. The gurgitation which occurs at every interruption in the uni formity of the flew. The two former of these interfering causes act upon water flowing in open channels, and have therefore to be taken into account in fixing the dimensions of those channels; but the last named cause acts exclusively upon water flowing in pipes. In the following remarks upon the flow in pipes it must, however, always be understood that they are supposed to run full bore, and to have got perfectly "in train," to use a technical phrase; that is to say, it is supposed that a constant velocity is maintained in those portions of the pipes wherein there are no side branches.
Now, the friction on the sides of the pipes depends principally upon their diameters, and upon their lengths, and upon the pressures upon the respective orifices of supply and discharge ; and as the latter con ditions (the pressures) are in fact analogous to the effect of a column of water, or "a head," as it is commonly called, it is customary to reason upon the pressures in terms expressing the heights of such columns. Practically it appears that the results obtained by allowing fur the above cited elements of the resistance produced by friction, require to be affected by a term deprn ling upon the initial velocity of the water ; and according to some Tee, iuvestigations by M. Dupuit, by another term depending upon the material of the pipe. For ordinary purposes it is often not necessary to take these causes of diminished supply into account, and it then suffices to consider that the quantity of water flowing through a pipe of uniform diameter, receiving its water from a reservoir at a high level, and discharging it into another reservoir at a lower level, the pipe being without any change of direction, may be represented by the formula Q=c H —11' in which q= the quantity sought ; difference of level between the extreme orifices; X= the length of the pipe ; li=the initial head; n'= the head over the lower orifice ; to= the diameter of the pipe; and c= a coeffi cient ascertained by experiment when the velocity of flow, per second, is as follows :— tion to the length and diameter of the pipes, he makes lt'= (0'01482 + / ; the result being in feet.
viT d 2g The friction, and the consequent loss of head, from the existence of bends, is found to he in a certain proportion dependent upon the ratio of the diameter of the tube to the radius of curvature of its axis.
Navier says, that the formula _ (0'00391 + 0'0186) (in which 29 r = the radius of the curvature, and a = the development of the arc), will represent the loss of head thus occasioned ; and according to him it would appear that is proportional to the square of the mean velocity, and to the length of the arc ; that it is a function of the radius of the are, and independent of the diameter of the pipes; and that It, decreases in proportion as r increases. In order to apply the above formula to the case of side mains branching off from a leading main, it is necessary to adopt the following ratios between the diameters and the radii ; The interference with the rate of delivery of a pipe by the gurgitation produced by the changes in the conditions of flow, may practically be neglected in the calculations for proportioning the details of a town distribution ; because it is easy to effect the pumping in the leading main with sufficient regularity to avoid its serious occurrence, and to make the distributing mains large enough to destroy its influence. Attention has, however, been called to this interference on account of the lesson it affords of the danger of adhering too strictly to the dimensions of pipes which would appear to be indicated by abstract theoretical laws ; and of the necessity which exists for providiog for irregular disturbing causes. There is another danger to be encountered in the delivery of water through long leading mains, namely, the danger arising from the accumulation of air in the bends, especially when they are in a vertical direction, for the air then has a tendency to accumulate at the summit of the bend, and thus either to diminish the water way, or even to stop the passage of the water altogether. The remedy for this evil consists in the establishment of air-vessels upon the summit of the bends, through which the air may escape ; and any slight retardation of flow created by the small quantity of air left in the water, or by the dead weight of the small column to be lifted, must be provided for by increasing the initial velocity of flow. In important works it is customary net only to introduce air-vessels, but also pressure regulators at the summit of the large bends, in order to ensure equality of flow. Fig. 1. represents a very simple air-valve which has been successfully applied.