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 1: / Line 1: @@
-The amount flowing in or out of inlets is calculated for the cell the inlet resides on.
+[[inlet (Water Overlay)|Inlet]]s 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.__NOTOC__
-When calculating '''inlets''', first the capacities are calculated.
+The amount flowing in or out of {{Inlets}} is calculated for the cell the {{Inlet}} resides on.
-If a T<sub>lower</sub> is defined:
+''Case 1: '''Inlet''':''<br>
-: ''C<sub>inthres</sub> = max( 0 , T<sub>lower</sub> - WL<sub>surface</sub> )''
+When calculating {{Inlets}}, first the capacities are calculated.
-If a I<sub>Q</sub> is defined:
+If a lower threshold <math>T_{l,t}</math> is defined:
-: ''C<sub>speed</sub> = Δt * I<sub>Q</sub>''
+: <math>Q_{lth} = A \cdot max( 0 , T_{l,t} - w_t )</math>
-If a C<sub>total</sub> is defined:
+If a positive inlet <math>q_t</math> is defined:
-: ''C<sub>incap</sub> = C<sub>used</sub> - C<sub>total</sub>''
+: <math>Q_p = \Delta t \cdot q_t</math>
-After calculating the capacities, the actual water inflow is calculated.
+If a capacity <math>Q_{total}</math> is defined:
-: ''Δw = max( 0 , min( C<sub>inthres</sub> , C<sub>speed</sub> , C<sub>incap</sub> ) ) / cell''
+: <math>Q_c = Q_{total}- \sum_{0..t-1}Q_i</math>
-: If any of the terms are undefined, they are not included.
+After calculating the capacities, the actual water inflow is calculated. If any of the terms are undefined, they are not included.
+: <math>\Delta w = \frac { max( 0 , min( Q_{lth}, Q_p , Q_c ) )}{A}</math>
-When calculating '''outlets''', first the capacities are calculated.
+''Case 2: '''Outlets''':''<br>
+When calculating outlets, first the capacities are calculated.
-If a T<sub>lower</sub> is defined:
+If an upper threshold <math>T_{u,t}</math> is defined:
-: ''C<sub>outthres</sub> = min( 0 , T<sub>upper</sub> - WL<sub>surface</sub> )''
+: <math>Q_{uth} = A \cdot min( 0 , T_{u,t} - w_t )</math>
-If a I<sub>Q</sub> is defined:
+If a negative inlet <math>q_t</math> is defined:
-: ''C<sub>speed</sub> = Δt * I<sub>Q</sub>''
+: <math>Q_p = \Delta t \cdot q_t</math>
-If a C<sub>total</sub> is defined:
+If a capacity <math>Q_{total}</math> is defined:
-: ''C<sub>outcap</sub> = -C<sub>total</sub> - C<sub>used</sub>''
+: <math>Q_c = -Q_{total} - \sum_{0..t-1}Q_i</math>
-After calculating the capacities, the actual water ouflow is calculated.
-: ''Δw = min( 0 , max( C<sub>outthres</sub> , C<sub>speed</sub> , C<sub>outcap</sub>) ) / cell''
-: If any of the terms are undefined, they are not included.
-After the water flow (either inflow or outflow) is computed, the capacity is updated.
-: ''C<sub>used</sub> (new) = C<sub>used</sub> (old) + (Δw * cell)''
+After calculating the capacities, the actual water outflow is calculated. If any of the terms are undefined, they are not included.
+: <math>\Delta w = \frac { min( 0 , max( Q_{uth} , Q_p, Q_c) ) } {A}</math>
 Where:
+* <math>w_t</math> = The [[Surface water level formula (Water Overlay)|water level]] on the surface relative to {{datum}}, at time t.
+* <math>T_{l,t}</math> = The [[Inlet lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the {{Inlet}} at time t.
+* <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 formula (Water Overlay)|timestep]].
+* <math>Q_{total}</math> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] of the {{Inlet}}.
-* Δw = The amount of water flow which takes place.
+* <math>Q_{0..n}</math> = The calculated previous amounts of flow.
-* Δt = Computational timestep.
+* <math>Q_{lth}</math> = The volume of water needed to reach the [[Inlet lower threshold (Water Overlay)|LOWER_THRESHOLD]] at the {{Inlet}}'s location.
-* cell = Cell size.
+* <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}}.
-* C<sub>speed</sub> = The amount of water inflow (or outflow when negative) possible based on the inlet's {{inlink|INLET_Q}} attribute.
+* <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).
-* C<sub>incap</sub> = The amount of water inflow possible based on the total {{inlink|INLET_CAPACITY|capacity}} of the inlet.
+* <math>\Delta w</math> = The amount of water flow which takes place.
-* C<sub>outcap</sub> = The amount of water outflow possible based on the total {{inlink|INLET_CAPACITY|capacity}} of the outlet.
-* C<sub>inthres</sub> = The amount of water inflow desired based on the inlet's {{inlink|LOWER_THRESHOLD}} attribute.
-* C<sub>outthres</sub> = The amount of water outflow desired based on the outlet's {{inlink|UPPER_THRESHOLD}} attribute.
-* WL<sub>surface</sub> The water level on the surface, relative to {{datum}}.
+==Related==
-* C<sub>total</sub> = The {{inlink|INLET_CAPACITY}} attribute of the inlet.
+The following topics are related to this formula.
-* I<sub>Q</sub> = The {{inlink|INLET_Q}} attribute of the inlet.
+; Structures
-* T<sub>lower</sub> = The {{inlink|LOWER_THRESHOLD}} attribute of the inlet.
+: [[Inlet (Water Overlay)|Inlet]]
-* T<sub>upper</sub> = The {{inlink|UPPER_THRESHOLD}} attribute of the inlet.
+; Models
+: [[Surface model (Water Overlay)|Surface model]]
-{{Template:WaterOverlay_nav}}
+{{WaterOverlay formula nav}}

Inlet formula (Water Overlay): Difference between revisions

Latest revision as of 11:08, 14 October 2026

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