_Supposing a sewer to have a gradient of 1 in 300, how much would the velocity and discharge be increased by altering the gradient to 1 in 100?_ 1 in 300 = 17·6 in mile. 1 in 100 = 52·8 in mile. As h is not given, we must assume it = 1∕4, as it does in circular sewers running full or half full. v = 55 √(h x 2f) = 55 √(35·2∕4) = 163 feet per minute. v^{1} = 55 √(104∕4) = 281 „ „ The increase in discharge may be similarly calculated. _Describe the relation existing in a sewer between gradient, volume, velocity, and size._ By the formula v = 55 √(_h.f._) Where v = velocity in feet per minute. h = hydraulic mean depth = (area of cross section of stream) ─────────────────────────────── (wetted perimeter). f = fall in feet in two miles. In circular sewers h = diameter/4. Thus the velocity varies as the square root of h or f. The volume discharged varies with the value of the factor v × s where s = sectional area of stream. If h remains constant, with a varying volume of s, then the volume discharged may remain constant. Thus h and v in a circular sewer are the same, whether the sewer runs full or half full. In a V-shaped channel the velocity remains the same whatever the depth of the stream, as its bed and area preserve the same proportions. An egg-shaped sewer approximates the V shape in form. Similar volumes of sewage have velocities which vary not only with the amount of fall, but the size of the sewer. The friction, as represented by the wetted perimeter, would be much less with sewage half filling a circular sewer, than with the same amount of sewage forming a broad shallow stream on the invert of a large sewer. CHAPTER XXVIII. THE DISPOSAL OF SEWAGE. The water-carriage system of sewage is, as the late Dr. Parkes put it, “the cleanest, the readiest, the quickest, and in many cases the most inexpensive method.” But when the sewage is conveyed to the outfall of the sewer, its ultimate disposal is still one of the most difficult problems of the present day. Various plans have been adopted, of which the following are the chief:— 1. Discharge into running water. 2. Discharge into the sea. 3. Separation of solid and liquid parts {By settlement. {By precipitation. 4. Filtration through various artificial media or through land. 5. Irrigation. 6. Bacterial methods.