Inlet formula (Water Overlay)

Inlets are hydraulic structures can pump water in and out of the project area and are connected with a water body outside the project area.

The amount flowing in or out of Inlets is calculated for the cell the Inlet resides on.

Case 1: Inlet:
When calculating Inlets, first the capacities are calculated.

If a lower threshold ${\displaystyle T_{l,t}}$ is defined:

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

If a positive inlet q Qt is defined:

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

If a capacity Qtotal is defined:

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

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

${\displaystyle \Delta w={\frac {max(0,min(Q_{lth},Q_{t},Q_{c}))}{A}}}$

Case 2 Outlets:
When calculating outlets, first the capacities are calculated.

If an upper threshold Tu,t is defined:

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

If a negative inlet q Qt is defined:

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

If a capacity Qtotal is defined:

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

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

${\displaystyle \Delta w={\frac {min(0,max(Q_{uth},Q_{t},Q_{c}))}{A}}}$

Where:

• ${\displaystyle w_{t}}$ = The water level on the surface relative to datum, at time t.
• ${\displaystyle T_{l,t}}$ = The LOWER_THRESHOLD of the Inlet at time t.
• ${\displaystyle T_{u,t}}$ = The UPPER_THRESHOLD of the Inlet at time t.
• ${\displaystyle q_{t}}$ = The INLET_Q of the Inlet at time t.
• ${\displaystyle \Delta t}$ = Computational timestep.
• ${\displaystyle Q_{total}}$ = The INLET_CAPACITY of the Inlet.
• ${\displaystyle Q_{0..n}}$ = The calculated previous amounts of flow.
• ${\displaystyle Q_{lth}}$ = The desired lower water level at the Inlet's location, based on the LOWER_THRESHOLD of the Inlet.
• ${\displaystyle Q_{uth}}$ = The desired upper water level at the outlet's location, based on the outlet's UPPER_THRESHOLD of the Inlet.
• ${\displaystyle Q_{t}}$ = The amount of water inflow (or outflow when negative) possible based on the INLET_Q of the Inlet and timestep ${\displaystyle \Delta t}$.
• ${\displaystyle Q_{c}}$ = The total amount of water inflow (or outflow when negative) allowed based on the total capacity of the Inlet.
• ${\displaystyle A}$ = Size of the Inlet/outlet area in m2, based on the amount of cells and cell size. Current implementation only has one cell.
• ${\displaystyle \Delta w}$ = The amount of water flow which takes place.

Related

The following topics are related to this formula.

Structures
Inlet
Models
Surface model