Inlet formula (Water Overlay): Difference between revisions

Latest revision as of 11:08, 14 October 2026

Inlets are hydraulic structures that 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_{l t h} = A \cdot m a x (0, T_{l, t} - w_{t})

If a positive inlet $q_{t}$ is defined:

Q_{p} = Δ t \cdot q_{t}

If a capacity $Q_{t o t a l}$ is defined:

Q_{c} = Q_{t o t a l} - \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.

Δ w = \frac{m a x (0, m i n (Q_{l t h}, Q_{p}, Q_{c}))}{A}

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

If an upper threshold $T_{u, t}$ is defined:

Q_{u t h} = A \cdot m i n (0, T_{u, t} - w_{t})

If a negative inlet $q_{t}$ is defined:

Q_{p} = Δ t \cdot q_{t}

If a capacity $Q_{t o t a l}$ is defined:

Q_{c} = - Q_{t o t a l} - \sum_{0.. t - 1} Q_{i}

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

Δ w = \frac{m i n (0, m a x (Q_{u t h}, Q_{p}, Q_{c}))}{A}

Where:

$w_{t}$ = The water level on the surface relative to datum, at time t.
$T_{l, t}$ = The LOWER_THRESHOLD of the Inlet at time t.
$T_{u, t}$ = The UPPER_THRESHOLD of the Inlet at time t.
$q_{t}$ = The INLET_Q of the Inlet at time t.
$Δ t$ = Computational timestep.
$Q_{t o t a l}$ = The INLET_CAPACITY of the Inlet.

$Q_{0.. n}$ = The calculated previous amounts of flow.
$Q_{l t h}$ = The volume of water needed to reach the LOWER_THRESHOLD at the Inlet's location.
$Q_{u t h}$ = The volume of water that must be removed to reach the UPPER_THRESHOLD at the outlet's location.
$Q_{p}$ = The amount of water inflow (or outflow when negative) possible based on the INLET_Q of the Inlet and timestep $Δ t$ .
$Q_{c}$ = 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 number of cells and cell size (currently calculated per cell).
$Δ w$ = The amount of water flow which takes place.

The following topics are related to this formula.

Structures: Inlet
Models: Surface model

Models

Surface • Ground • Rain • Evapotranspiration • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas

Timestep • Season • Surface water level • Groundwater level
Flow formulas

Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas

Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related

Building attributes • Hydrological features • Hydraulic structures • Terrain attributes • Model attributes • Prequels • Results • Simulation data

@@ Line 7: / Line 7: @@
 If a lower threshold <math>T_{l,t}</math> is defined:
-: <math>Q_{lth} = max( 0 , T_{l,t} - w_t )</math>
+: <math>Q_{lth} = A \cdot max( 0 , T_{l,t} - w_t )</math>
 If a positive inlet <math>q_t</math> is defined:
@@ Line 18: / Line 18: @@
 : <math>\Delta w = \frac { max( 0 , min( Q_{lth}, Q_p , Q_c ) )}{A}</math>
-''Case 2 '''Outlets''':''<br>
+''Case 2: '''Outlets''':''<br>
 When calculating outlets, first the capacities are calculated.
-If an upper threshold T<sub>u,t</sub> is defined:
+If an upper threshold <math>T_{u,t}</math> is defined:
-: <math>Q_{uth} = min( 0 , T_{u,t} - w_t )</math>
+: <math>Q_{uth} = A \cdot min( 0 , T_{u,t} - w_t )</math>
 If a negative inlet <math>q_t</math> is defined:
@@ Line 42: / Line 42: @@
 * <math>Q_{0..n}</math> = The calculated previous amounts of flow.
-* <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_{lth}</math> = The volume of water needed to reach the [[Inlet lower threshold (Water Overlay)|LOWER_THRESHOLD]] at the {{Inlet}}'s location.
-* <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_{uth}</math> = The volume of water that must be removed to reach the [[Inlet upper threshold (Water Overlay)|UPPER_THRESHOLD]] at the outlet's location.
 * <math>Q_p</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}}.
-* <math>A</math> = Size of the {{Inlet}}/outlet area in m<sup>2</sup>, based on the amount of cells and cell size. Current implementation only has one cell.
+* <math>A</math> = Size of the {{Inlet}}/outlet area in m<sup>2</sup>, based on the number of cells and cell size (currently calculated per cell).
 * <math>\Delta w</math> = The amount of water flow which takes place.

Inlet formula (Water Overlay): Difference between revisions

Latest revision as of 11:08, 14 October 2026

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