experiment expressing the proportion which the loss of head by friction bears to the height due to the velocity, and the formula becomes

Supposing it be required to find the velocity for the flow of liquid at two different inclinations, the velocity in the one case being given, it is easy to find the other, for the velocity will vary inversely as the square roots of the fall.

For example, if the velocity in a sewer is 65 ft. per second with a fall of 25 ft. in 100, and it is desired to know what would the velocity be if the same sewer had a fall of 4 ft. in 100, it may be stated as follows: as 4: 65 :: √25 26 ft. per second, for the

=

2

square root of 4 is 2 and the square root of 25 is 5, and of 65 = 26 ft. per second, or putting it the converse way, supposing a fall of 4 ft. per 100 gives a velocity of 26, what will a fall of 25

5 2

in the same length produce? then × 2665 ft. per second.

If a fall of 1 in 100 gives a velocity of 13 ft. per second, what will be the velocity if the same pipe is placed perpendicularly?

In this latter case the fall is of course 100, then

130 ft. per second.

√100
√1

× 13

=

If again the question is put as follows: A sewer laid with a fall of 9 ft. in 100 gives a velocity of 39 ft. per second, what will be the velocity in a sewer of the same size laid with a fall of per mile?

1 ft.

This is a formula which has recently been simplified by Mr. R. Hering. The original formula reads:

1

1 Engineers' Club, Philadelphia, June, 1888; Sanitary News, December, 1888.

v = velocity in feet per second.

n = coefficient of roughness of wetted perimeter. r = hydraulic radius.

s = slope of water surface.

rs.

by substituting for the value s the least grade that we are likely to have in sewers-namely, 1:2500. Then we obtain the constant 0.00281 0.0004

value:

(2)

=

7.0, which reduces the formula to:

This substitution influences the result but little. It tends to make the smaller sewers slightly larger than the original formula. There would be in fact no difference at all for a sewer about 13 ft. in diameter, whatever its grade, and the difference would increase, as the size diminishes and the grade increases, up to an excess of about 5 per cent. for a sewer of 1 ft. diameter, at a grade of 4 ft. for 100. This excess of about 5 per cent. is practically the maximum error for sewer application, and it is always on the safe side.

But the formula can still further be simplified by substituting a numerical value for n.

According to Kutter, for glazed pipe we would have to put n = '010. But owing to the frequency of joints and the imperfect shape due to the process of burning, which causes projection in the sewer at nearly every joint, it is not safe to assume so low a coefficient. Besides, the flow of sewage is slower than that of clear water, because the suspended matter drags at the perimeter and tends to hold the water back. Allowing for these causes we generally get nearer the truth if for pipe-sewers we put n = 013.

For brick sewers, on the other hand, Kutter gives n = '013. It has been found, however, that if well built n can often be reduced to 012. Still, for sewage flow, the resistance is again greater, and Hering finds that by adopting the value of n = 013 also for brick sewers we are about as nearly correct as it is necessary to be in the majority of cases, and err slightly on the safe side, if we err at all.

By substituting this value in formula 2 we get:

which is, therefore, not only a sufficiently accurate, but also a sufficiently simple, formula for general use in sewer work. Stated in general terms, the formula reads:

By substituting the following values for the coefficients A and B, it can be used for any other degree of roughness than n = '013 as may be thought proper.

For very smooth and regularly-shaped sewers we might say;

CHAPTER XIX.

DISPOSAL OF SEWAGE.

(157) Irrigation of Land.

THERE are two kinds of irrigation, "broad irrigation" and "intermittent filtration," These are thus distinguished by the Royal Commissioners on Sewage Discharge: "Broad irrigation means the . distribution of sewage over a large surface of ordinary agricultural ground, having in view a maximum growth of vegetation (consistently with due purification) for the amount of sewage supplied. Filtration means the concentration of the sewage, at short intervals on an area of specially chosen porous ground, as small as will absorb and cleanse it; not excluding vegetation, but making the produce of it of secondary importance. The intermittency of application is a sine quâ non even in suitably constituted soils, wherever complete success is aimed at."

In broad irrigation, the sewage is simply delivered in special channels on to the land, which should be well drained, and vegetables and crops grown thereon; it is a plan well adapted to certain villages and small towns, where local circumstances are favourable.

The best soil is that of a sandy loam, its successful application requires about 1 acre to every 120 of the population. Broad irrigation has been lately carried out on a large scale at Berlin. English examples are Croydon, Cheltenham, and Blackburn.

Intermittent downward filtration, has been for some years the favourite method of dealing with sewage, the sewage going on to the filter beds in the crude state, or after first previous precipitation, the beds receive the effluent; a very perfect method of purification is secured by this last process.

The principle of making filter beds for intermittent filtration

may be exemplified by a brief description of those at MerthyrTydvil (population 14,500), 20 acres of land are used for the filtering areas.

The sewage is first treated with lime, and is strained in special tanks through cinders; it then flows on to the conduit which conveys it to the filtering areas, these last being arranged on a plan devised by Mr. Bailey Denton. The land is a loamy soil, 18 in. thick overlaying a bed of gravel. The whole area is underdrained to a depth of from 5 to 7 ft. Lateral drains placed at regular distances the one from the other run towards the main or effluent drain, which drain is everywhere 6 ft. deep. The surface of the land has been formed into beds; these slope towards the main drain with a fall of 1: 150. The surface is ploughed into ridges; on these, vegetables are planted or seeds sown; the line of the ridged furrow is in the direction of the under drain. Along the raised margin of each bed in each area delivering carriers are placed, one edge being slightly depressed. The strained sewage passes from the conduits into the delivering carriers, and as it overflows the depressed edges, runs gently into and along the furrows down to the lowest and most distant part of the plot. The sewage

continues to be so delivered for six hours; then an interval of rest for eighteen hours takes place and again the land is thoroughly charged with the fertilising stream. The water percolates through the 6 ft. of earth, and reaches the lateral drains, which convey it to the main effluent drain. In addition to this land, used as filtering areas, there are a number of acres laid out for irrigation.

Intermittent irrigation is now carried on largely both at home and abroad, with the most satisfactory results as regards purity of effluent, but with varying results as to the money value of the resulting crops, in some cases a considerable return being received, in others the returns have not been satisfactory; this is what might be expected, the conditions of the soil and other things varying.

One of the most unsuitable lands for intermittent irrigation is a stiff clay soil, but even here it is stated that a good filter bed can be constructed at a cost of about £600 to £800 per acre by burning the clay into ballast and laying down the ballast to a depth of about 3 ft. with layers of alluvial or other rich soil interposed.