Drainage formula (Water Overlay)

Depending on whether the drainage is passive or active, the formula for either passive or active drainage is used.

Drainage passive

First the flow capacity is calculated

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$ Q_{b}=A_{d}\cdot f_{s}\cdot {\frac {||w_{d}-w_{w}||\cdot A_{w}}{A_{d}\cdot f_{s}+A_{w}}} $

if $ w_{d}>w_{w} $ then:

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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): Q_t = min ( Q_p, Q_b , Q_d )

else:

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$ Q_{t}=min(Q_{p},Q_{b},Q_{w}) $

Where:

$ q_{t} $ is the DRAINAGE_Q of the Drainage at time t.

$ \Delta t $ is the computational timestep.

$ w_{d} $ is the ground water level, above the drainage, in meters.

$ w_{w} $ is the water level in the waterway.

$ z_{d} $ is the drainage datum height in meters.

$ z_{w} $ is the max waterway height.

$ A_{d} $ is the drainage area size in square meters.

$ A_{w} $ is the waterway area size in square meters.

$ f_{s} $ is the average storage percentage of the ground above the drainage.

$ Q_{p} $ is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep $ \Delta t $.

$ Q_{b} $ is the amount transferred for a balanced ground and surface water level.

$ Q_{d} $ is the amount of water available in the ground above the drainage.

$ Q_{w} $ is the amount of water available in the waterway.

$ Q_{t} $ is the actual drained, or infiltrated backwards, volume at time t.

Drainage active

Case 1: Active Draining:

If a positive DRAINAGE_Q is defined:

$ Q_{p}=\Delta t\cdot q_{t} $

$ Q_{d}=(w_{d}-z_{d})\cdot f_{s} $

If an overflow threshold $ T_{o,t} $ is defined as well:

$ Q_{o}=max(0,T_{o,t}-w_{w}) $

The actual water pumped out of the drainage system is calculated. If any of the terms are undefined, they are not included.

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Case 2: Active Reverse Draining:

If a negative DRAINAGE_Q is defined:

$ Q_{p}=\Delta t\cdot q_{t} $

$ Q_{w}=min(0,z_{w}-w_{t,w}) $

If an overflow threshold $ T_{o,t} $ is defined as well:

$ Q_{o}=min(0,T_{o,t}-w_{t,w}) $

The actual water pumped into the drainage system is calculated. If any of the terms are undefined, they are not included.

$ Q_{t}=max(0,max(Q_{p},Q_{w},Q_{o})) $

Where:

$ q_{t} $ is the DRAINAGE_Q of the Drainage at time t.

$ \Delta t $ is the computational timestep.

$ Q_{p} $ is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep <math<\Delta t</math>.

$ w_{d} $ is the ground water level, above the drainage, in meters.

$ w_{w} $ is the water level in the waterway.

$ z_{d} $ is the drainage datum height in meters.

$ z_{w} $ is the waterway's datum height.

$ f_{s} $ is the average storage percentage of the ground above the drainage.

$ Q_{d} $ is the amount of water available in the ground above the drainage.

$ T_{o,t} $ is the overflow threshold in meters at time t.

$ Q_{o} $ is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.

$ Q_{w} $ is the amount of water available in the waterway.

$ Q_{t} $ is the actual drained (or pumped) volume at time t.

Notes

• A negative DRAINAGE_Q can potentially raise the ground water level at the drainage so much that it reaches the surface above the drainage.

Related

The following topics are related to this formula.

Structures

Drainage (Water Overlay)

Models

Surface model (Water Overlay)

Ground model (Water Overlay)

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