Errors of the kinematic wave and diffusion wave approximations are derived for non-uniform, time-independent cases of planar or channel flow under three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation is found to be accurate for KF 2 0≥5, where K is the kinematic wave number and F 0 is the Froudel number. However, in order for the kinematic wave approximation to be sufficiently accurate, KF 2 0 may have to be significantly greater than 5. The accuracy of the diffusion wave approximation is significantly influenced by the downstream boundary condition.
Introduction
In an overland flow a steady state is attained for constant rainfall of sufficiently long duration (greater than or equal to the time of concentration t c), because the depth of flow at the outlet increases until equilibrium is reached. The same is true for flow in a channel subject to constant lateral inflow....
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Singh, V.P., Aravamuthan, V. (1998). Accuracy of hydrodynamic approximations in hydrology: Non-uniform, steady flow. In: Encyclopedia of Hydrology and Lakes. Encyclopedia of Earth Science. Springer, Dordrecht . https://doi.org/10.1007/1-4020-4497-6_3
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DOI: https://doi.org/10.1007/1-4020-4497-6_3
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