the liquid to land, with a view to its purification, would be by intermittent filtration. We have reason to believe that sufficient land, of a quality suitable for this purpose, exists within a convenient distance of the northern outfall. The liquid portion of the sewage would be pumped up to this land from the separating works, and after filtration would be conducted to the river.

"12. We do not know whether suitable land, in sufficient quantity, can be found in convenient positions near the southern outfall. If not, the liquid must be conveyed across to the north side by a conduit under the river.

"13. If suitable land, in sufficient quantity and at reasonable cost, cannot be procured near the present outfalls, we recommend that the sewer liquid, after separation from the solids, be carried down to a lower point of the river, at least as low as Hole Haven, where it may be discharged. In this case, it will also be advisable that the liquid from the southern sewage should be taken across the river, and the whole conveyed down the northern side. It may be found that the separating process can be effected more conveniently at the new than at the present outfalls; this will depend on various considerations of cost and otherwise.

"14. If the outfalls are removed further down the river, the main conduit or conduits may, if thought desirable, be made of sufficient capacity to include a general extension of the drainage to the whole of the districts round London, as recommended by Sir Joseph Bazalgette and Mr. Baldwin Latham. In new drainage works, the sewage should be, as far as possible, separated from the rainfall."

CHAPTER XVIII.

CALCULATIONS OF THE DISCHARGE OF SEWAGE OR WATER OR OTHER LIQUIDS.

(154) Eytelwein's Formula.

THE formula for calculating the velocity of discharge, the quantity of cubic feet per minute, and other data, are most accurately obtained by the use of Eytelwein's formulæ, the formulæ having been tested by experiment and found to agree closely.

=

=

Let d the diameter of the pipe in inches, Q the quantity of water in cubic feet per minute, the length of the pipe in feet, and h the difference of level between the surface of the water in the reservoir and at the end of the pipe, or the head; any three of the quantities being known, the fourth may be calculated by the following formulæ.

(1) d =

'0448 Q2 (l +4·2d)

h

These formulæ are much easier worked by logarithms. Expressed logarithmetically they become :

(1) log d = [2 log +2·6515 + log (1 + 4·2d) — log h]. (2) log Q = {1·3485 + log h + 5 log d― log (l +4·2d)} (3) log 13485 + log h+ 5 log d-2 log [neglecting

4.2d.]

=

(4) log h= 2 log Q+2.6515 + log (l + 4·2d) — 5 log d.

The following are examples of the application of formulæ 2 and 4, taken from Mr. Henry Law's useful treatise on logarithms:

What quantity of water will be discharged by a pipe 18 inches in diameter, 5,371 feet long, and under a head of 75 feet?

Ans. 761-9 cubic feet per minute.

"What head will be required to force 350 cubic feet per minute through a pipe 15.5 inches in diameter, and 3,640 feet long Ans. 22 739 feet."

The above formulæ give the rate of discharge in pipes under pressure; but in the case of drains and sewers it is most frequently required to ascertain both the velocity and rate of discharge when only partially filled. Putting D for the diameter in feet of a circular sewer, L for the length in feet in which the sewer falls one foot, v the velocity in feet per minute, Q the quantity discharged in cubic feet per minute, and c and s co-efficients the values of which for every tenth of the diameter are given in the table below, then

ON I

and, Qs,

Q = 3√√√ T

L

In the case of an oval sewer, of the usual form in which the radii of the crown, sides, and invert are respectively equal to 1,

1 and, the height of the sewer being 1, putting H for the height of the sewer in feet, and e and k co-efficients the values of which for every tenth of the height are given in the table below, the values of the other letters being the same as before, then

In the case of a circular sewer the velocity is greatest when filled to 81 hundredths of the diameter, and the quantity discharged is greatest when filled to 95 hundredths of the same; and in that of an oval sewer the greatest velocity is when filled to 85 hundredths of the height, and the greatest discharge when filled to 96 hundredths of the same.

As an example, what will be the velocity and rate of discharge in a circular sewer 2 feet in diameter, having a fall of 1 in 500, when filled to a height of four-tenths of its diameter ?

Therefore the velocity will equal 165 feet per minute, and the quantity discharged 194 cubic feet in the same time.

(155) Head of Water.

The terms "head" of water, " total head," "loss of head," are technical, and apply to height of water. Thus with a pipe 20 feet high connected with a reservoir which has 6 feet of water in it; if the pipe be filled, at the orifice of the tap, there would be a pressure of water, equal to the height of the water above the orifice of the tap and this would be a head equal to 26 feet. It could however be proved, that the theoretical velocity due to a column 26 feet high, at this point would not be quite attained, because of the more or less rough state of the interior of the pipe; this is expressed by loss of head due to friction. The pressure of water in the pipe just considered is called "hydrostatic pressure," to distinguish it from "hydraulic pressure," which is the pressure in flowing water, the other being the pressure in still water. There is an important distinction between the two, for in the latter the pressure is generally a changing pressure; for instance, in the case of the cistern being emptied, as the level of the water lowered there would be a continual "loss of head."

Supposing that there is, no friction, the loss of head in producing a given increase of velocity is equal to the height of vertical fall which would produce the same increase of velocity in a body falling freely; this may be expressed as the loss of head equals the height due to the acceleration; if the particle start from a state of rest, that height is called the height due to the velocity, and is given by the following formula, where v equals the velocity in feet per second, and h the height in feet.

=

Then v8.025 /h; and if h = 20, then v = 8·025 × 4·47 = 35.87. If friction is taken into account a co-efficient F is got out by