And for any velocity beyond 78 inches per second, c=21043. 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 IC + re = _(the previous notation being retained), then, v, the velocity = 0'1541131 + V0'023751 + 32806'6 x 4 D . 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 haul, without any allowauce for friction, r, or expressing it in terms of the height n= If, then II will be the portion of the 2y Lead 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 e, the wet contour a, and the two coefficients it is necessary to introduce respectively, a and b; the expression cX of the resistance would become a be) ; and we 'should have n 2g o = be). It is then only necessary to ascertain the value of the coefficients a, b, in order to apply the formula for general use ; but unfortunately every observer has attached different values to them. In this state of uncertainty it is sufficient to adopt the formula and values attached to the coefficients by Woisbach, in his Treatise on Mechanics,' because the formula is simple, and is known to give safe that is to say, results which are rather in excess of those ascertained by direct experiment, but sufficiently accurate for practical perpo.es. Weisbach calls the loss of head h'; and confining his atten The fortnulm for calculating the discharge of pipes under certain fixed conditions of bead and diameter, cease to be applicable when there is a series of branch-mains, sub-mains, and serviee-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 adopted by Mr. Hawksley may perhaps be cited as the. one most generally satisfactory, and it has been described by himself by saying, that upon the constant delivery system (in which the pipes are always 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. lie then allows for a loss of bead of 4 feet in every 200 yards; and adopt, in the diameters to be given to the pipes, the I q . .
formula d = I3 ,/ A I ; q = the number of gallons to be delivered ; I a-- the length of the main in yards; It the head in feet ; and d, the diameter required, in inches. In Glanders ' Formulas h rm.:age des Inganieurs; there is to be found a description of a more elaborate and theoretically correct method of ascertaining the diameters of sub-mains; but it is so much more complicated than the one used by Mr. Hawkaley, that it will suffice for the purposes of this Cycloptedia to refer the reader to the work in which it is explained.
In carrying into effect a town distribution It is necessary to observe numerous precautions, in order to protect the pipes from injury by external causes. Thus, wherever gas- and water-pipes are laid in to one another the water-pipes should be laid at a lower evel than those conveying gas. In England it is sufficient to place the gas-pipes at about two feet from the surface of the pavement; but in order to protect the water-pipes from the effect of frost, it is neces eery to place them at least 4 feet below the same lave); and in the latitudes of Berlin, or of St. Petersburg, it has been found that water-pipes have been frozen at even 6 feet from the surface of the ground. In towns wherein the street traffic is exceptionally heavy the vibrations of the ground may also require that the pipes should be laid at a considerable depth, and indeed this detail may be considered to vary in almost every case. It would appear that when the pipes are laid at about, 4 feet from the surface in our latitudes, the tempe rature of the water as it leaves the pipes will be sensibly the same, at all seasons of the year, with its temperature at the moment of entry, provided the motion be maintained in the pipes uniformly ; and it thence follows that ono of the best precautions which can be adopted against frost is to maintain a coustant circulation in the pipes. The dilatation of the pipes from an increase of temperature must be taken into acsount in laying down any system of town dietrib. Con ; and it would appear from M. Girard's direct experiments that the average rate of dilatation is equal to 0.00000300223 of a foot for every addi tional degree of Fahrenheit's' scale. when the pipes are free, and in the open air. In the ground M. Girard found that the temperatures of the pipes were functions of the difference of temperatures of the surreuuding media ; but that they were nearer to the temperature of tie ground than to that of the water. The tendency of some
waters to produce deposits in the pipes they traverse must also bo taken into account, as it may affect the discharge in a very serious manner ; in some instances, in Yorkshire, the bores of the leading mains have been known to have been thus diminished in a few years to one half their sectional area by the deposition of the hydrous oxide of iron; in mains supplied directly from chalk or limestone springs the same effect may be produced by the deposition of the bicarbonate of lime. 31. Payen states also that the slightly alkaline and aerated waters are those which are the moat likely to produce a development of tiffierettles of the hydrous oxide of iron in the interior of pipes of that metal: and that the oxidation takes place more rapidly upon gray cast-iron than upon the whiter varieties. It appears from experi ment, and frorn the reeults obtained in practice, that by coating the interior of water-pipet with a solution of hydraulic lime, or with lin seed oil containing litharge, the formation of the tiffiereilles before mentioned will be retarded; and in London the precaution of thus coating the pipes is universally adopted. The chloride of sodium when present in the water in small quantities, it may be added, facilitates the formation of the tuberculea Until within a few years the distribution of water to the private consumers was effected by the intermittent system, or by means of a supply panel through the etreotebains, at certain hours of the day, into cisterns placed in the houses, where it was stored for domestic use as might be required. The cisterns, in such cases, are made with fioatevalves, such as the common ball-cock, fly 2, or the lever-valve, ill. 3, which close the delivery-pipes when the water attains definite levels: and, in addition to these means of stopping the supply when a suffieicmt quantity of water has been delivered the cietei its are pro shied with an open overflow pipe connected with the drainage of the honses, through which the excels+ of water may pule it the machinery for intercepting the flow should not act. It 13 found, however, that, in the find place, there is so lunch carelessness ill the manner in which the cistern/tare fixed and maintained in order, that the quality of the water it very li tile to be contaminated in private houses. The great cisterns are, in fact, too often placed close to water closets or sinks; the service-p.pes to the watsr-cleseta often form a direct commuuiea tion between the pans of the closets and the water In the cisterns, so that the gases frotu the one must escape through the other ; tiro cisterns are too often made of improper materials; they are left exposed far too often to receive atmospheric impurities, dust, or soot ; and, incredible as it may eolit!, it is very rarely index.] that cisterns are cleaned out from one year's end to another. The host water in the world so treated must be rendered more ur less unfit for human con sumption; and it was priucipally to avoid this evil that the constant delivery system *as introduced, avowedly because that system allowed the cisterns to be dispensed with altogether. But it was alsu asserted that the constant-delivery system would effect an economy in the supply of water, because it is found practically that in the lower class of dwellings the ball-cocks are either stolen or tied up. so that the excess of water was forcedly passed through the waste. or overflow pipe during a great portion of the time the street mains were under charged. Unfortunately the economy has not been attained ; on the contrary, whenever the water supply of a town has remained in the Lands of a municipality, it is found to be so difficult to maintain the necessary control and supervision over the distributary apparatus, that the waste upon the constant-delivery system has proved to be so enormous that the system has practically been abandoned in many cases. It really would appear that the only means by which the abuses of the otherwise perfect method of delivery under constant pressure could be prevented would be by enforcing the sale of water by meter ; and, indeed, aim water is nearly as valuable as gas, there can he no reason for selling the one by measure and not the other. Gas, in London, costa 4s. 6d. per 1000 cubic feet; water, at the rate of 6d. per 1000 gallons, costs 3s. 1'33d per 1000 cubic feet. But hitherto no water-teeter has been devised by means of which the water can bo measured without intercepting the pressure; so that at preeent there appears to be an almost Insuperable difficulty in the way of the intro duction of the constant-delivery system in many towns about to con struct water-works de sore. In towns like London, the difficulties which would attend the modifications of the existing domeetic arrange ments of the water-pipes would be so great, that it is to be feared the present evils of the intermittent system will continue to le borne for many years still to come.