Drainage formula (Water Overlay)

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:

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

$Q_{g,t}=w_{g,t}-z_{d}$

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

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

After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.

$\Delta w={\frac {max(0,min(>Q_{g,t},Q_{o,t},Q_{p,t}))}{A}}$

Case 2: Active Reverse Draining:

If a negative Pump q is defined:

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

If a lower threshold T_l,t is defined as well:

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

If an upper threshold T_u,t is defined as well:

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

If a capacity Q_total is defined:

$Q_{c}=Q_{total}-abs(\sum _{0..t-1}Q_{i})$

After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.

$\Delta w={\frac {max(0,max(Q_{l,t},Q_{u,t},Q_{t},-Q_{c}))}{A}}$

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

Related

The following topics are related to this formula.

Structures

Drainage

Models

Surface model

Underground model

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