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:

$w_{t}$ = 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.
$\Delta t$ = Computational timestep.
$Q_{total}$ = The INLET_CAPACITY of the Inlet.

$Q_{0..n}$ = 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 1: / Line 1: @@
-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.__NOTOC__
+[[inlet (Water Overlay)|Inlet]]s are hydraulic structures can pump water in and out of the project area and are connected with a water body outside the project area.__NOTOC__
-The amount flowing in or out of inlets is calculated for the cell the inlet resides on.
+The amount flowing in or out of {{Inlets}} is calculated for the cell the {{Inlet}} resides on.
-'''Inlets:'''<br>
+''Case 1: '''Inlet''':''<br>
-When calculating inlets, first the capacities are calculated.
+When calculating {{Inlets}}, first the capacities are calculated.
-If a lower threshold T<sub>l</sub> is defined:
+If a lower threshold <math>T_{l,t}</math> is defined:
-: ''Q<sub>lth</sub> = max( 0 , T<sub>l,t</sub> - w<sub>t</sub> )''
+: <math>Q_{lth} = max( 0 , T_{l,t} - w_t )</math>
-If a positive Inlet q is defined:
+If a positive inlet q Q<sub>t</sub> is defined:
-: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''
+: <math>Q_t = \Delta t \cdot Q_t</math>
 If a capacity Q<sub>total</sub> is defined:
-: ''Q<sub>c</sub> = Q<sub>total</sub>''- ΣQ<sub>0..t-1</sub>
+: <math>Q_c = Q_{total}- \sum_{0..t-1}Q_i</math>
 After calculating the capacities, the actual water inflow is calculated. If any of the terms are undefined, they are not included.
-: ''Δw = max( 0 , min( Q<sub>lth</sub> , Q<sub>t</sub> , Q<sub>c</sub> ) ) / A''
+: <math>\Delta w = \frac { max( 0 , min( Q_{lth}, Q_t , Q_c ) )}{A}</math>
-'''Outlets:'''<br>
+''Case 2 '''Outlets''':''<br>
 When calculating outlets, first the capacities are calculated.
-If an upper threshold T<sub>u</sub> is defined:
+If an upper threshold T<sub>u,t</sub> is defined:
-: ''Q<sub>uth</sub> = min( 0 , T<sub>u</sub> - w<sub>t</sub> )''
+: <math>Q_{uth} = min( 0 , T_{u,t} - w_t )</math>
-If a negative Inlet q is defined:
+If a negative inlet q Q<sub>t</sub> is defined:
-: ''Q<sub>t</sub> = Δt * q<sub>t</sub>''
+: <math>Q_t = \Delta t \cdot Q_t</math>
 If a capacity Q<sub>total</sub> is defined:
-: ''Q<sub>c</sub> = -Q<sub>total</sub> - ΣQ<sub>0..t-1</sub>''
+: <math>Q_c = -Q_{total} - \sum_{0..t-1}Q_i</math>
 After calculating the capacities, the actual water ouflow is calculated. If any of the terms are undefined, they are not included.
-: ''Δw = min( 0 , max( Q<sub>uth</sub> , Q<sub>t</sub> , Q<sub>c</sub>) ) / A''
+: <math>\Delta w = \frac { min( 0 , max( Q_{uth} , Q_t, Q_c) ) } {A}</math>
-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)''
 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 desired lower water level at the {{Inlet}}'s location, based on the [[Inlet lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the {{Inlet}}.
-* cell = Cell size.
+* <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}}.
-* A = area of the inlet/outlet
+* <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>.
-* C<sub>speed</sub> = The amount of water inflow (or outflow when negative) possible based on the inlet's [[Inlet q (Water Overlay)|INLET_Q]] attribute.
+* <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>incap</sub> = The amount of water inflow possible based on the total [[Inlet capacity (Water Overlay)|capacity]] of the inlet.
-* C<sub>outcap</sub> = The amount of water outflow possible based on the total capacity of the outlet.
-* C<sub>inthres</sub> = The amount of water inflow desired based on the inlet's [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] attribute.
-* C<sub>outthres</sub> = The amount of water outflow desired based on the outlet's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] attribute.
-* WL<sub>surface</sub> = The water level on the surface, relative to [[Datum|datum]].
+* <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.
-* C<sub>total</sub> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] attribute of the inlet.
+* <math>\Delta w</math> = The amount of water flow which takes place.
-* I<sub>Q</sub> = The INLET_Q attribute of the inlet.
-* T<sub>l</sub> = The LOWER_THRESHOLD attribute of the inlet.
-* T<sub>u</sub> = The UPPER_THRESHOLD attribute of the inlet.
-==See also==
+==Related==
-* [[Inlet (Water Overlay)|Inlet]]
+The following topics are related to this formula.
+; Structures
+: [[Inlet (Water Overlay)|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 13:09, 5 March 2024

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