In low-lying sewers where the outfall is impeded, mechanical aids are required to prevent blocking of the sewers. This may be obtained by pumping at the outfall, to enable sewage to escape at all conditions of the tide, or to raise the sewage on to land for irrigation. In the =Shone system= the sewage is raised to the required height by means of compressed air. In this system the sewage is received into “ejectors.” These are cylindrical reservoirs, in which is a float on a counterpoised lever. When a certain quantity of sewage has entered, a valve opens admitting the compressed air, which forcibly raises the sewage into a higher length of sewer or to the outfall. CHAPTER XXVII. PROBLEMS AS TO FLOW IN SEWERS. In order to prevent deposit of solid matter, sewers should be constructed with a sufficient gradient, and of a shape which presents the least surface for friction in proportion to the amount of liquid to be conveyed. All brick sewers should be egg-shaped, with the narrow end downwards. The egg is formed by two circles touching one another, the diameter of the upper circle being twice that of the lower. This shape possesses the great advantage that when the depth of the stream is diminished the amount of wetted surface of sewer (_wetted perimeter_) is diminished in equal proportion, whereas in every other form of sewer it is relatively increased. Thus the friction, which depends on the extent of the wetted perimeter, is kept down to a minimum. Where, as in outfall sewers, the volume of sewage is large, and does not vary greatly in amount, the circular form may be preferable, as it is cheaper and stronger than the egg-shaped sewer. Below 18 inches internal diameter, sewers should be circular in section, and made of stoneware, not brick. The _velocity of flow_ depends upon (1) the hydraulic mean depth of the stream, and (2) its inclination or fall. The _hydraulic mean depth_ means the depth of a rectangular channel whose sectional area (and therefore the volume of whose current) equals that of the curved sewer or pipe, concerning which the calculation is made, and whose width equals the entire wetted perimeter of the sewer or pipe. It is thus equal to sectional area/wetted perimeter. In the case of circular pipes, if we take the diameter to be 1, and assume the pipe to be running full, the sectional area = πr^2, where π = 3·1416 and r = half diameter. The wetted perimeter = 2πr, that is, the circumference of the circle formed by the pipe. Therefore hydraulic mean depth = h = πr^2∕2πr = 1∕4 Similarly when the pipe runs half full— h = (πr^2∕2)/(2πr) = 1∕4 The solution of problems where a smaller arc of a circle is occupied by fluid requires trigonometrical methods, and is not usually needed in practice.