The overflow weir and the leaping weir have no moving parts and are used for the regulation of the flow in sewers. A leaping weir is formed by a gap in the invert of a sewer through which the dry weather flow will fall and over which a portion or all of the storm flow will leap. One form of leaping weir is shown in Fig. 43. An overflow weir is formed by an opening in the side of a sewer high enough to permit the discharge of excess flow into a relief channel. A weir at San Francisco is shown in Fig. 44. A series of tests were run on leaping weirs and overflow weirs in the hydraulic laboratory of the University of Illinois. The type of leaping weir tested was formed by the smooth spigot end of a standard vitrified sewer pipe. The overflow weirs were formed by a steel knife edge in the side of the pipe parallel to its axis as shown in Fig. 45. Tests were made in 18–inch and 24–inch pipes on various slopes from 0.018 to 0.005, for both leaping weirs and overflow weirs. The overflow weirs were varied in length from 16 inches to 42 inches and were placed at various heights from 25 per cent to 50 per cent of the diameter above the invert of the sewer. As the result of the observations the following formulas were developed. For the leaping weir the expressions for the coordinates of the curve of the surfaces of the falling stream, are: For the outside surface _x_ = 0.53_V_^⅔ + _y_^{4⁄7} For the inside surface _x_ = 0.30_V_^{4⁄7} + _y_^¾ in which _x_ and _y_ are the coordinates. The origin is in the upper surface of the stream vertically above the end of the invert of the pipe. The ordinate _y_ is measured vertically downwards. _V_ is the velocity of approach in feet per second. These expressions are applicable to any diameter of sewer up to 10 or 15 feet. They should _not_ be used for depths of flow greater than about 14 inches; nor for slopes of more than 25 per 1,000; nor for velocities less than 1 foot per second nor more than 10 feet per second. The expression for the ordinate of the inside curve is not good for less than 6 inches nor more than 5 feet. The expression for the ordinate of the outside curve is limited to values between the origin and 5 feet below it. The expression for the length of an overflow weir of the type shown in Fig. 45, necessary to discharge a given quantity, is in the form, _l_ = 2.3_Vd_ log _h__{1}⁄_h__{2} in which _l_ = the length of the weir in feet; _V_ = the velocity of approach in feet per second; _d_ = the diameter of the pipe in feet; _h__{1} = the head of water on the upper end of the weir; _h__{2} = the head of water on the lower end of the weir.