Ali S. Fayad, Discoverer of The Explicit Alternate Flow Depth in Rectangular Open Channels

Force on Closed Sluice Gate

If a sluice gate is closed shut and the water behind it is static then a hydrostatic force acts on the gate. This force is the resultant of the hydrostatic pressure on the vertical gate. The fictitious hydrostatic pressure resultant is said to be located at a depth from the  surface that is 2/3 of the water surface elevation above the invert of the channel.

In contrast, once the gate is raised to a new position, to allow flow to proceed past it, the value and depth of the new force resultant on the gate change from the hydrostatic values to  new values.

 Force on Opened Sluice Gate

The theoretical force on a frictionless sluice gate, as derivable from the conservation of the momentum equation, is available in the hydraulic literature (Sellin, RHJ, 1969)

The introduction of the Fayad explicit form of the alternate flow depths ratio permits a clear analytical representation of the force on the sluice gate in terms of the upstream Froude and the hydrostatic force (itself a function of the upstream depth. This verifies in a closed-form functional relationship that the theoretical force on a sluice gate, under steady state conditions, is less than the hydrostatic force on the full upstream depth.