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

A closed sluice gate within the path of a rectangular open channel can eventually overtop to serve as a weir. Alternatively, an open-sluice gate may become inundated to serve in a dual mode. This hybrid mode of combined underflow and overflow effectively implies that the sluice gate has also become a weir.

The weir depth is the physical depth of the weir from its top to its base irrespective of whether the gate is open or closed. It is equal to the physical (material) depth of the sluice gate. The weir height above the invert equals the weir depth (or sluice gate depth) plus the height of the gate opening when the gate is lifted for underflow.  The following examines weir flow:

CHANNEL: Rectangular Weir

1- A sharp-crested weir obstructs water in a rectangular channel. It causes 0.223 cfs of overflow above the top of the weir. The height of the weir is at 1.75 ft above the bottom of the channel. The width of the channel is 1.5 ft. Upstream of the weir, where the water surface initiates downward curvature, the head on the weir is measured at 0.1 ft above the crest.

Analyze with MNEMOSYNE

SOLUTION:

Geometric & Physical Properties:

(a) total flow = 0.223 cfs, (b) weir depth =1.75 ft, (c) breadth = 1.5 ft, (d)head on the weir is 0.1 ft.

Results:

(a) The approach velocity =0.08 fps, (b)height of water upstream behind the weir = 1.85 ft., (c)the weir coefficient =7.04., (d) the discharge coefficient =0.87745

Interpretation:

The results assume that the downstream face of the weir remains ventilated. The surface of the water curves as it approaches the face of the weir indicating that the water at the surface is experiencing a horizontal acceleration due to a constriction of the flow area constrained by the conservation of flow-mass. The narrowest area of the flow occurs in the nappe immediately downstream of the crest. The weir coefficient is based on the simplified formula: CW=Q/H^1.5, where Q is the total flow and H is the head on (or above the crest of ) the weir.

Verification:

The weir discharge coefficient is expected to be below unity since it corrects for the effect of viscosity and the effect of the contraction of the flow in the immediate downstream vicinity of the weir.

OPEN CHANNEL:  RECT. WEIR
[$] GIVEN INPUT: lb, ft

[Q]  Total Flow = .223
[Y] Weir Head: H= .1
    Weir Height: yw= 1.75

[B] Breadth:  b = 1.5

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OPEN CHANNEL:  RECT. WEIR
Assuming weir-downstream remains ventilated
`Discharge coefficient = .8774508
`Weir coefficient (C is Q/H^1.5) = 7.041509
`Height of water upstream behind weir = 1.85
`Approach velocity = 8.036036E-02
`Theoretical Hydrostatic Force on Weir = 159.705
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