Gravity-driven flow over a round-crested weir is analyzed for viscous flow. An equation for the entire flow profile is obtained by simplifying the equations for slowly varying film thickness, assuming a velocity profile, and integrating across the film. Solution of the resulting first order, ordinary differential equation requires a boundary condition generated at a critical point of the flow, beyond which waves cannot propagate upstream. Results for the relationship between head and flow rate are consolidated on a dimensionless master curve represented by an empirical equation.

Issue Section:
Research Papers
Topics:
Flow (Dynamics), Thin films, Boundary-value problems, Differential equations, Film thickness, Gravity (Force), Viscous flow, Waves
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