# CEM88(D) : Weir / Orifice (high sill elevation)

**Figure 18. Device schematic view**

### Weir - Free flow ( and )

**[12]**

Classical equation for the free flow weir ().

### Weir - Submerged ( and )

**[13]**

Classical formulation for the submerged weir.

The free-flow/submerged transition takes place for

Thus,

for

The equivalent free-flow coefficient can be calculated:

It indicates the degree of submergence of the weir by comparing it to the introduced free-flow coefficient . In effect, the reference coefficient of the device considered is that corresponding to the free-flow weir ( close to ).

### Orifice - Free flow ( and )

An equation of the following type is applied:

**[14]**

This formulation is applicable to large width rectangular orifices.

The continuity towards the open-channel flow is assured when:

, one then has: .

### Orifice - Submerged

Two formulations exist, according to whether the flow is partially submerged or completely submerged.

#### Partially submerged flow ( and )

**[15]**

#### Totally submerged flow ( and )

**[16]**

This is the classic equation of the submerged orifice with .

The operation of the weir/orifice device is represented by the above equations and in figure 19. Whatever the conditions of pipe flow, one calculates an equivalent free-flow coefficient, corresponding to the free-flow orifice:

(12): Weir - Free flow

(15): Orifice - Partially submerged

(13): Weir - Submerged

(16): Orifice - Totally submerged

(14): Orifice - Free flow

**Figure 19. Weir - Orifice**

Equations are also available in a Matlab script file (function Qouvrage) here.