Abstract
The boundary layer theory for the smooth open channel was apllied to the gradually contracted open channel flow. Then the decrease of layer thickness and the variation of velocity profile along the flow were investigated.
According to the theory, the relation between δ, the layer thickness from side wall, and ζ, the layer thickness from bed is shown as η=βξ(η=δ/b, ξ=ζ/h, β=(h/b) r, h;depth, b; a half of width), in the process of layer development, but in the last state of uniform flow h≅b the relation becomesη≅βξ.When a steady state flow in which the layer has developed fully contracts its cross-section, the layer begins to decrease its thickness. If η>, βξ, η alone varies with ξ=1 and since η=βξ, η varies together with ξ.
In the gradually contracted open channel, the more the cross-section varies, the more rapidly the layer thickness decreases, despite of η=βξ or η>βξ. When the variation of cross section is same, the layer thickness in the channel with side contraction (db/dx<O, dh/dx<O) decreases more rapidly than in the channel with weir (db/dx=0, dh/dx<0).
Then, the equation for the layer thickness and the approximate graphical solution in the channel with weir is shown.
From this solution, it is shown that the layer decreases sooner for larger discharge under the same weir height or for higher weirs under the same discharge.
