Weir formula (Water Overlay)

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Flow across weirs is calculated differently for free flow and submerged flow.

The height of the water at each end of the weir, relative to the weir, is calculated:

Based on the relative water heights, the weir is judged to have either a submerged flow or a free flow, based on the following ratio:

if

For free flow, capacity is calculated directly:

For submerged flow, the following calculation is used:

Finally the actual amount of water flow is calculated:

Where:

  • = The height of the water column relative to the top of the weir, on the side with the highest water level.
  • = The height of the water column relative to the top of the weir, on the side with the lowest water level.
  • = The water level on the left side of the weir, relative to datum.
  • = The water level on the right side of the weir, relative to datum.
  • = The WEIR_HEIGHT of the weir.
  • = Dutch weir factor, set to 1.7.
  • = The WEIR_COEFFICIENT of the weir.
  • = The WEIR_WIDTH of the weir.
  • = The potential rate of water flow across the weir.
  • = The ratio of water heights on either side of the culvert.
  • = The potential rate of water flow across the weir, based on a free flow calculation.
  • = The potential rate of water flow across the weir, based on a submerged calculation.
  • = Loss coefficient for submerged weirs, set to 0.9.
  • = Flow area, based on the highest water column height relative to the top of the weir, and WEIR_WIDTH of the weir.
  • = Acceleration factor of GRAVITY, defined for the Water Overlay.
  • = The water flow which takes place.
  • = Computational timestep.
  • = Cell size.

Related

The following topics are related to this formula.

Structures
Weir
Models
Surface model