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:

WHsource = max(0, max( WLleft, WLright ) - WHweir)
WHdest = max(0, min( WLleft, WLright ) - WHweir)

For free flow, capacity is calculated directly:

Cfree = DWF * WC * WW * ( WHsource - WHdest )3/2

For submerged flow, a culvert-like calculation is used:

Csubmerged = U * A * sqrt( 2 * G * (WHsource - WHdest) )

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:

WHrelative = WHdest : WHsource
C = min( Csubmerged , Cfree) if WHrelative > 0,5
C = Cfree otherwise

Finally the actual amount of water flow is calculated:

Δw = Δt * C / cell

Where:

  • Δw = The water flow which takes place.
  • Δt = Computational timestep.
  • cell = Cell size.
  • C = The potential rate of water flow across the weir.
  • WHrelative = The ratio of water heights on either side of the culvert.
  • Cfree = The potential rate of water flow across the weir, based on a free flow calculation.
  • Csubmerged = The potential rate of water flow across the weir, based on a submerged calculation.
  • WHsource = The height of the water column relative to the top of the weir, on the side with the highest water level.
  • WHdest = The height of the water column relative to the top of the weir, on the side with the lowest water level.
  • U = Loss coefficient for submerged weirs (0,9).
  • A = Flow area, based on the highest water column height relative to the top of the weir, and the weir width, defined by the WEIR_WIDTH attribute of the weir
  • G = Acceleration factor of gravity
  • DWF = Dutch weir factor, set to 1.7
  • WC = The WEIR_COEFFICIENT attribute of the weir.
  • WHweir = The WEIR_HEIGHT attribute of the weir.
  • WLleft = The water level on the left side of the weir, relative to datum.
  • WLright = The water level on the right side of the weir, relative to datum.

See also

Template:WaterOverlay nav