The hydraulic jump is a phenomenon which is seldom considered in sewer design. If not guarded against it may cause trouble at overflow weirs and at other control devices, in grit chambers, and at unexpected places. The causes of the hydraulic jump are sufficiently well understood to permit designs that will avoid its occurrence, but if it is allowed to occur the exact place of the occurrence of the jump and its height are difficult, if not impossible, to determine under the present state of knowledge concerning them. The hydraulic jump will occur when a high velocity of flow is interrupted by an obstruction in the channel, by a change in grade of the invert, or the approach of the velocity to the “critical” velocity. The “critical” velocity is equal to √(_gh_), where _h_ is the depth of flow and _g_ is the acceleration due to gravity. The velocity in the channel above the jump must be greater than √(_gh__{ 1}), where _h__{ 1} is the depth of flow in the channel above the jump. The velocity in the channel below the jump must be greater than √(_gh__{ 2}), where _h__{ 2} is the depth of flow below the jump. The jump will not take place unless the slope of the invert of the channel is greater than _g_⁄_C_^2,in which _C_ is the coefficient in the Chezy formula. With this information it is possible to avoid the jump by slowing down the velocity by the installation of drop manholes, flight sewers, or by other expedients.
The shape of the drop-down curve can be expressed, in some cases, by mathematical formulas of more or less simplicity, dependent on the shape of the conduit. The formula for a circular conduit is complicated. Due to the assumptions which must be made in the deduction of these formulas, the results obtained by their use are of no greater value than those obtained by approximate methods. A method for the determination of the drop-down curve is given by C. D. Hill.[32] In this method it is necessary that the rate of flow past all sections shall be the same; that the depth of submergence at the outlet shall be known; and that the depth of flow at some unknown distance up the stream shall be assumed. The shape and material of construction of the sewer and the slope of the invert should also be known. The problem is then to determine the distance between cross-sections, one where the depth of flow is known, and the other where the depth of flow has been assumed. This distance can be expressed as follows: