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I'm looking for an analytical solution to the open channel rectangular fluid flow profile. The flow is bounded by three walls but the top is open to atmosphere. Assume steady state flow that is parallel and incompressible.

**I've already found information involving a rectangular flow channel bounded by 4 rectangular plates(top closed):****Geometry**: Infinite along x direction. y ranges from -w to w and z ranges from -h to h. z denotes depth of our channel.

-If w=h, we have parabolic flow along y axis(along any given plane within depth z). Flow drops off as you approach rectangular walls at y= -w or +w.

-As w/h becomes very large(e.g w/h ≥ 10) , velocity profile flattens along centre of y axis and falls off very close to the walls(within distance h from either wall). Flow along the y direction is almost uniform until we are very close to the side walls. We also get parabolic flow in z direction within this limit of w>>h.

Any help would be much appreciated.