# 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

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

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

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

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

${\displaystyle Q_{t}=min(Q_{p},Q_{b},Q_{d})}$

else:

${\displaystyle Q_{w}=A_{w}\cdot (w_{w}-z_{w})}$

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

Where:

${\displaystyle q_{t}}$ is the DRAINAGE_Q of the Drainage at time t.
${\displaystyle \Delta t}$ is the computational timestep.
${\displaystyle w_{d}}$ is the ground water level, above the drainage, in meters.
${\displaystyle w_{w}}$ is the water level in the waterway.
${\displaystyle z_{d}}$ is the drainage datum height in meters.
${\displaystyle z_{w}}$ is the max waterway height.
${\displaystyle A_{d}}$ is the drainage area size in square meters.
${\displaystyle A_{w}}$ is the waterway area size in square meters.
${\displaystyle f_{s}}$ is the average storage percentage of the ground above the drainage.
${\displaystyle Q_{p}}$ is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep Δt.
${\displaystyle Q_{b}}$ is the amount transferred for a balanced ground and surface water level.
${\displaystyle Q_{d}}$ is the amount of water available in the ground above the drainage.
${\displaystyle Q_{w}}$ is the amount of water available in the waterway.
${\displaystyle Q_{t}}$ is the actual drained, or infiltrated backwards, volume at time t.

## Drainage active

Case 1: Active Draining:

If a positive DRAINAGE_Q is defined:

${\displaystyle Q_{p}=\Delta t\cdot q_{t}}$
${\displaystyle Q_{d}=(w_{d}-z_{d})\cdot f_{s}}$

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

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

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

${\displaystyle Q_{t}=max(0,min(Q_{d},Q_{o},Q_{p}))}$

Case 2: Active Reverse Draining:

If a negative DRAINAGE_Q is defined:

${\displaystyle Q_{p}=\Delta t\cdot q_{t}}$
${\displaystyle Q_{w}=min(0,z_{w}-w_{t,w})}$

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

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

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

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

Where:

${\displaystyle q_{t}}$ is the DRAINAGE_Q of the Drainage at time t.
${\displaystyle \Delta t}$ is the computational timestep.
${\displaystyle Q_{p}}$ is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep Δt.
${\displaystyle w_{d}}$ is the ground water level, above the drainage, in meters.
${\displaystyle w_{w}}$ is the water level in the waterway.
${\displaystyle z_{d}}$ is the drainage datum height in meters.
${\displaystyle z_{w}}$ is the waterway's datum height.
${\displaystyle f_{s}}$ is the average storage percentage of the ground above the drainage.
${\displaystyle Q_{d}}$ is the amount of water available in the ground above the drainage.
${\displaystyle T_{o,t}}$ is the overflow threshold in meters at time t.
${\displaystyle Q_{o}}$ is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.
${\displaystyle Q_{w}}$ is the amount of water available in the waterway.
${\displaystyle Q_{t}}$ 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)
Underground model (Water Overlay)