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:

hs = max(0, max( wl, wr ) - zw)
hd = max(0, min( wl, wr ) - zw)

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:

hratio = hd / hs
C = min( Csubmerged , Cfree) if hratio > 0,5
C = Cfree otherwise

For free flow, capacity is calculated directly:

Cfree = fw,d * cw * ww * ( hs - hd )3/2

For submerged flow, the following calculation is used:

Csubmerged = Uloss * A * sqrt( 2 * g * ( hs - hd ) )

Finally the actual amount of water flow is calculated:

Δw = Δt * C / Δx

Where:

  • hs = The height of the water column relative to the top of the weir, on the side with the highest water level.
  • hd = The height of the water column relative to the top of the weir, on the side with the lowest water level.
  • wl = The water level on the left side of the weir, relative to datum.
  • wr = The water level on the right side of the weir, relative to datum.
  • zw = The WEIR_HEIGHT of the weir.
  • fw,d = Dutch weir factor, set to 1.7.
  • cw = The WEIR_COEFFICIENT of the weir.
  • ww = The WEIR_WIDTH of the weir.
  • C = The potential rate of water flow across the weir.
  • hratio = 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.
  • Uloss = Loss coefficient for submerged weirs, set to 0.9.
  • A = Flow area, based on the highest water column height relative to the top of the weir, and WEIR_WIDTH of the weir.
  • g = Acceleration factor of GRAVITY, defined for the Water Overlay.
  • Δw = The water flow which takes place.
  • Δt = Computational timestep.
  • Δx = Cell size.

Related

The following topics are related to this formula.

Structures
Weir
Models
Surface model