 CEM88(V) : Weir / Undershot gate (small sill elevation) Figure 18. Device schematic view

Weir - Free-flow Weir - Submerged with coefficient of reduction for submerged flow.

The flow reduction coefficient is a function of and of the value of this ratio at the instant of the free-flow/submerged transition. The submerged conditions are obtained when . The law of variation of the coefficient has been derived from experimental results ( ).

Let :

If : If : With One calculates an equivalent coefficient for free-flow conditions as before.

Undershot gate - Free-flow It has been established experimentally that the undershot gate discharge coefficient increases with . A law of variation of of the following form is adopted: avec : Hence, In order to ensure the continuity with the open channel free-flow conditions for , we must have: Hence, for Undershot gate - Submerged

Partially submerged flow  being the same as for open channel flow.

The following free-flow/submerged transition law has been derived on the basis of experimental results:  In order to ensure continuity with the open channel flow conditions, the free-flow/submerged transition under open channel conditions has to be realized for instead of in the weir/orifice formulation.

Totally submerged flow The equation is the same as the one for where is replaced by (and by ) for the calculation of the coefficient and (and therefore for the calculation of ).

The transition to totally submerged flow occurs for: with: ( )

The functioning of the weir / undershot gate device is represented by the above equations and displayed in figure 20. Whatever the conditions of the pipe flow, one calculates an equivalent free-flow discharge coefficient, corresponding to the classical equation for the free-flow undershot gate. The reference coefficient introduced for the device is the classic coefficient of the free-flow undershot gate, usually close to . It is then transformed to which allows to compute and from equation  for the free-flow undershot gate.

Remark: it is possible to get , even under free flow conditions, since the discharge coefficient increases with the ratio. (12): Weir - Free flow
(19): Undershot gate - Partially submerged
(17): Weir - Submerged
(20): Undershot gate - Totally submerged
(18): Undershot gate - Free flow
Figure 20. Weir - Undershot gate

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