Inlet formula (Water Overlay): Difference between revisions

Latest revision as of 13:09, 5 March 2024

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 $T_{l,t}$ is defined:

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

If a positive inlet q Q_t is defined:

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

If a capacity Q_total is defined:

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.

\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 T_u,t is defined:

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

If a negative inlet q Q_t is defined:

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

If a capacity Q_total is defined:

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.

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

Where:

$Q_{0..n}$ = The calculated previous amounts of flow.
$Q_{lth}$ = The desired lower water level at the Inlet's location, based on the LOWER_THRESHOLD of the Inlet.
$Q_{uth}$ = The desired upper water level at the outlet's location, based on the outlet's UPPER_THRESHOLD of the Inlet.
$Q_{t}$ = The amount of water inflow (or outflow when negative) possible based on the INLET_Q of the Inlet and timestep $\Delta t$ .
$Q_{c}$ = The total amount of water inflow (or outflow when negative) allowed based on the total capacity of the Inlet.

$A$ = Size of the Inlet/outlet area in m², based on the amount of cells and cell size. Current implementation only has one cell.
$\Delta w$ = The amount of water flow which takes place.

@@ Line 38: / Line 38: @@
 * <math>T_{u,t}</math> = The [[Inlet upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the {{Inlet}} at time t.
 * <math>q_t</math> = The [[Inlet q (Water Overlay)|INLET_Q]] of the {{Inlet}} at time t.
-* <math>\Delta t</math> = Computational timestep.
+* <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)|timestep]].
 * <math>Q_{total}</math> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] of the {{Inlet}}.
@@ Line 44: / Line 44: @@
 * <math>Q_{lth}</math> = The desired lower water level at the {{Inlet}}'s location, based on the [[Inlet lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the {{Inlet}}.
 * <math>Q_{uth}</math> = The desired upper water level at the outlet's location, based on the outlet's [[Inlet upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the {{Inlet}}.
-* <math>Q_t</math> = The amount of water inflow (or outflow when negative) possible based on the [[Inlet q (Water Overlay)|INLET_Q]] of the {{Inlet}} and timestep Δt.
+* <math>Q_t</math> = The amount of water inflow (or outflow when negative) possible based on the [[Inlet q (Water Overlay)|INLET_Q]] of the {{Inlet}} and timestep <math>\Delta t</math>.
 * <math>Q_c</math> = The total amount of water inflow (or outflow when negative) allowed based on the total capacity of the {{Inlet}}.