Consideration on the boundary condition for calculations of open channel flow

The reason given for the boundary condition of calculation open channel flow leaves some insufficiencies. Calculation for tranquil flow is done toward upstream with downstream boundary condi-tion for depth, the reason is explained as the influence of downstream water level relating to wave propa-gation. But it is logically wrong since the discussion is based on the equation of steady flow without un-steady term. Mathematically, we have only to give boundary condition where the water depth is fixed and to proceed the calculation from the boundary condition position. Also, since the steady flow can be found by solving the governing equation for unsteady flow with steady boundary condition, boundary condition of the depth for steady flow calculation can be given in the same manner as for the analysis using the characteristic curve method. Boundary condition for free surface is obtained directly by equating the normal components of the velocities of water particles on the surface and of free surface variation.

open channel flow

water level calculation

boundary condition

steady flow equation

unsteady flow equation

free surface boundary condition