Modelling Sewer Hydraulics

Abstract

Conservation laws of mass, momentum and energy are used to describe open channel flow in sewers. The mass conservation principle yields the continuity equation, whereas Newton’s second law yields the momentum equation. Two flow variables in one-dimensional flow, such as the flow depth y and velocity V, or the flow depth y and the rate of discharge Q, are sufficient to define the flow conditions at a cross section. Therefore, two governing equations may be used to describe one-dimensional unsteady open channel flow. Except for the velocity distribution coefficient, α, and the momentum distribution coefficient, β, the momentum and energy equations are equivalent as shown in [4], provided that the flow depth and velocity are continuous. This condition is met if there are no flow discontinuities, such as a hydraulic jump or a bore. However, the momentum equation should be used for flows with discontinuities, since, unlike in the energy equation, it is not necessary to know the magnitude of losses at the discontinuities in the application of the momentum equation.