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CEM88(D) : Weir / Orifice (important sill)

CEM 88 D diagram

Weir - free flow

(h1<Wandh223h1)

Q=μFL2gh13/2

Classical formulation of the free flow weir (μF0.4).

Weir - submerged flow

(h1<W and h223h1)

Q=μSL2g(h1h2)1/2h2

Classical formulation of the submerged weir.

The switch from submerged to free flow occurs for h2=23h1, we then have:

μS=332μF for μF=0.4μS=1.04

An equivalent free flow coefficient can be calculated:

μF=QL2gh13/2

which makes it possible to evaluate the degree of flooding of the threshold by comparing it to the free coefficient μF introduces. Indeed, the master coefficient of the structure introduced is that of the free weir. (μF close to 0.4).

Orifice - free flow

(h1W and h223h1)

We take a formulation like:

Q=μL2g(h13/2(h1W)3/2)

This modeling applies well to large rectangular orifices.

Continuity to free surface operation is ensured when:

h1W=1, we then have μ=μF.

Orifice - submerged flow

There are two formulations depending on whether the orifice is partially submerged or totally submerged.

Partially submerged flow

(h1W and 23h1<h2<23h1+W3)

Q=μFL2g[332((h1h2)1/2h2)(h1W)3/2]

Totally submerged flow

(h1W and 23h1+W3<h2)

Q=μL2g(h1h2)1/2[h2(h2W)]Q=μL2g(h1h2)1/2W

Classical formulation of submerged orifices, with μ=μS.

Orifice weir operation is represented by the equations above and Figure 19. Regardless of the type of flow under load, an equivalent free flow coefficient is calculated corresponding to the conventional free orifice formulation:

CF=QL2gW(h10.5W)1/2

CEM 88 D chart

  • (12) : Weir - free flow
  • (15) : Orifice - partially submerged
  • (13) : Weir - submerged
  • (16) : Orifice - totally submerged
  • (14) : Orifice - free flow

Figure 19. Weir - Orifice