761 



WATER SUPPLY. 



WATER SUPPLY. 



762 



of their districts. These variable conditions are of much greater im- 

 portance than is generally considered to be the case ; for it appears 

 from careful examination that about three-fourths of the total daily 

 consumption of a town takes place between the hours of eight in the 

 morning and eight in the evening ; and experienced engineers make 

 their pipes and engines large and powerful enough to discharge one- 

 fourth of the total daily consumption in one hour. Evidently, then, it 

 must be desirable to employ the motive power which is able to adapt 

 itself to such variable demands with the greatest elasticity. 



In passing from the pumping station to the regulating reservoir, or 

 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 flow. 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 iii 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 for the 

 above cited elements of the resistance produced by friction, require to 

 be affected by a tjrm depi n ling upon the initial velocity of the water ; 

 and according to some recini investigations 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 <j = c * / - D 5 ; in which <i = the 



quantity sought; f=the difference of level between the extreme 

 orifices; A = the length of the pipe ; n = the initial head ; H' = the head 

 over the lower orifice ; D = 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 h'= (0-01482 + 

 0-017963\ I v" ., 



= \ . ; the result being in feet. 



^/ v j d 2</ 



The friction, and the consequent loss of head, from the existence of 

 bends, is found to be 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 A, = -!_(0-0039-L +0'0186) - (in which 



2g r r 



r = the radius of the curvature, aud a = the development of the arc), 

 will represent the loss of head thus occasioned ; and according to him 

 it would appear that A, 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 arc, and independent of the diameter of the pipes ; and 

 that A, 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 : 



And for any velocity beyond 78 inches per second, c=21'043. But 

 this formula can only be applied when the velocity is previously 

 known ; should this not be the case, or should it not be ascertainable by 

 actual observation, it may be calculated by a second formula in which 



making K = H + *~ H (the previous notation being retained), then, V, the 

 A 



velocity = - 0-1541131 + . /0'023751 + 32806-6 x POL. When it be- 



comes necessary to take the friction on the sides of the pipe into 

 account, it is ascertained by calling, firstly, the velocity due to the 

 vertical head, without any allowance for friction, v, or expressing it in 



terms of the height H= , then H will be the portion of the 



head destroyed in producing that velocity, or the loss of head pro- 

 duced by the friction. Secondly, if we call the length of the pipe 

 A, the sectional area s, the wet contour c, aud the two coefficients 

 it is necessary to introduce respectively, a and 6; the expression 



o\ 

 of the resistance would become a (i"+6); and we 'should have 



H =a (v 2 + &). It is then only necessary to ascertain the 



2y 8 



value of the coefficients a, 6, in order to apply the formula for general 

 use ; but unfortunately every observer has attached different values to 

 them. In this stato of uncertainty it is sufficient to adopt the formula 

 and values attached to the coefficients by Weisbach, in his ' Treatise 

 on Mechanics,' because the formula is simple, and is known to give safe 

 results; that is to say, results which are rather in excess of those 

 ancerUin^il by direct experiment, but sufficiently accurate for practical 

 .i-Ii call j the loss of head A' ; and confining his atten- 



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 etfect 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 9n 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 providing 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 tha 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 not only to introduce air-vessels, but 

 also pressure regulators at the summit of the large bends, in order to 

 ensure equality of flow. 1'iij. 1. represents a very simple air-valve 

 which has been successfully applied. 



The formula) for calculating the discharge of pipes under certain 

 fixed conditions of head and diameter, ceasa to be applicable when 

 there is a series of branch-mains, sub-mains, and service-pipes attached 

 to the leading main, such as always occurs beyond the service reser- 

 voirs, or the first point of distribution in a town supply. In fact the 

 dimensions to be given to the distributing pipes can hardly be decided 

 , upon other than upon empirical principles, and long experience is a 

 | better guide in these matters than any abstract theory. The method 

 i adopted by Mr. Hawksley may perhaps be cited as the one most 

 ! generally satisfactory, and it has been described by himself by saying, 

 j that upon the constant delivery system (in which the pipes are always 

 I under charge, and no cisterns are used), he divides the length of the 

 main in a street into portions of about 200 yards each, and he assigns 

 to every such portion the quantity of water it would be likely to 

 require, in proportion to the population to be supplied by it, on the 

 supposition that the total quantity is to be delivered within four hours. 

 He then allows for a loss of head of 4 feet in every 200 yards ; and 



