On the Velocity in Potential Flow along the Bottom Boundary of Sour at the Downstream Side of Sabo-dam
1980 Volume 32 Issue 4 Pages 24-32
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1980 Volume 32 Issue 4 Pages 24-32
The state of equilibrium of scour at the stream bottom may be produced when the frictional force of sand grain and the shearing force on the scoured bottom which is given by the boundary-layer at the bottom boundary keep balance. The boundary-layer is caused by the tractive force which the velocity in potential flow (the velocity outside the boundary-layer) produces in the neighbourhood of the bottom boundary in the scoured hole. On the other hand, the jet by overfall nappe impinges slant on the bottom boundary of scour and flow forwards as a two-dimensional wall jet. Therefore, the calculation of velocity in potential flow in the neighbourhood of the scoured bottom as a wall jet may be important to discuss the depth of scour by the overfall nappe at the downstream side of Sabo-dam. In this study, the stream line of the impinging jet flow which is produced by slanting submerget jet is estimated by using stream function, and it is shown as curved lines. The equation of velocity in potential flow in the neighbourhood of scoured bottom is derived by using the potential theory. This equation is finally written as:
u0/v0b=Aξ/(ξ2+Bξ+C)
where, u0 is the velocity of potential flow in the neighbourhood of the bottom, v0b(=u0 max) in the hypothetical impinging velocity of the submerged jet flow on the bottom, and ξ is the nondimensional length along the bottom boundary. Two kinds of models of bottom boundary, one of which is plain surface and the other is curved surface with the shape of scoured bottom, are prepared in this experiment. To those surfaces, grains of sand are glued as closely to each other as possible. The jet flow in this experiment is given in two-dimensional flow by the aerated free falling nappe from weir into the pool. The results of the experiments by the method described above show that the plots of measured values agree with the theoretical curve expressed by the above equation. The coefficients of the curve which are calculated from the measured data are discussed connecting with the hydraulic condition of flow.
