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

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

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

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

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

else:

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

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

Where:

$w_{g}$ is the ground water level in meters

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

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

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

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

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

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

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

$Q_{max}$ is the amount available in the ground above the drainage.

$Q_{p_{t}}$ is the drainage capacity at time t

$Q_{d}$ is the actual drained volume at time t

Drainage active

Case 1: Active Draining:

If a positive Pump q is defined:

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

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

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

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

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

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

Case 2: Active Reverse Draining:

If a negative Pump q is defined:

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

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

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

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

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

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

Where:

$w_{g}$ is the ground water level in meters

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

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

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

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

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

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

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

$Q_{max}$ is the amount available in the ground above the drainage.

$Q_{p_{t}}$ is the drainage capacity at time t

$Q_{d}$ is the actual drained volume at time t

Notes

A negative pump 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

Models

Surface model

Underground model

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