=33. Extent and Intensity of Storms.=—In the design of storm sewers it is necessary to decide how heavy a storm must be provided for. The very heaviest storms occur infrequently. To build a sewer capable of caring for all storms would involve a prohibitive expense over the investment necessary to care for the ordinary heavy storms encountered annually or once in a decade. This extra investment would lie idle for a long period entailing a considerable interest charge for which no return is easily seen. The alternative is to construct only for such heavy storms as are of ordinary occurrence and to allow the sewers to overflow on exceptional occasions. The result will be a more frequent use of the sewerage system to its capacity, a saving in the cost of the system, and an occasional flooding of the district in excessive storms. The amount of damage caused by inundations must be balanced against the extra cost of a sewerage system to avoid the damage. A municipality which does not provide adequate storm drainage is liable, under certain circumstances, for damages occasioned by this neglect. It is not liable if no drainage exists, nor is it liable if the storm is of such unusual character as to be classed legally as an act of God. Kuichling’s studies of the probabilities of the occurrence of heavy storms are published in Transactions of the American Society of Civil Engineers, Vol. 54, 1905, p. 192. Information on the extent of rain storms is given by Francis in Vol. 7, 1878, p. 224, of the same publication. Kuichling expresses the intensity of storms which will occur, once in 10 years as _i_ = 105⁄(_t_ + 20), once in 15 years as _i_ = 120⁄(_t_ + 20), in which _i_ is the intensity of rainfall in inches per hour and _t_ is the duration of the storm in minutes. CHAPTER IV THE HYDRAULICS OF SEWERS =34. Principles.=—The hydraulics of sewers deals with the application of the laws of hydraulics to the flow of water through conduits and open channels. In so far as its hydraulic properties are concerned the characteristics of sewage are so similar to those of water that the same physical laws are applicable to both. In general it is assumed that the energy lost due to friction between the liquid and the sides of the channel varies as some function of the velocity, usually the square, and that the total energy passing any section of the stream differs from the energy passing any other section only by the loss of energy due to friction. The general expression for the flow of sewage would then be, _h_ = (_f_)_V_^n,