Inlet formula (Water Overlay): Difference between revisions

Revision as of 16:14, 4 December 2020

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 Δt.
$Q_{c}$ = 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 16: / Line 16: @@
 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>
 ''Case 2 '''Outlets''':''<br>
@@ Line 22: / Line 22: @@
 If an upper threshold T<sub>u,t</sub> is defined:
-: ''Q<sub>uth</sub> = min( 0 , T<sub>u,t</sub> - w<sub>t</sub> )''
+: <math>Q_{uth} = min( 0 , T_{u,t} - w_t )</math>
 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>
 Where:
-* w<sub>t</sub> = The [[Surface water level formula (Water Overlay)|water level]] on the surface relative to {{datum}}, at time t.
+* <math>w_t</math> = The [[Surface water level formula (Water Overlay)|water level]] on the surface relative to {{datum}}, at time t.
-* T<sub>l,t</sub> = The [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the inlet at time t.
+* <math>T_{l,t}</math> = The [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the inlet at time t.
-* T<sub>u,t</sub> = The [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the inlet at time t.
+* <math>T_{u,t}</math> = The [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the inlet at time t.
-* q<sub>t</sub> = The [[Inlet q (Water Overlay)|INLET_Q]] of the inlet at time t.
+* <math>q_t</math> = The [[Inlet q (Water Overlay)|INLET_Q]] of the inlet at time t.
-* Δt = Computational timestep.
+* <math>\Delta t</math> = Computational timestep.
-* Q<sub>total</sub> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] of the inlet.
+* <math>Q_{total}</math> = The [[Inlet capacity (Water Overlay)|INLET_CAPACITY]] of the inlet.
-* Q<sub>0..n</sub> = The calculated previous amounts of flow.
+* <math>Q_{0..n}</math> = The calculated previous amounts of flow.
-* Q<sub>lth</sub> = The desired lower water level at the inlet's location, based on the [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the inlet.
+* <math>Q_{lth}</math> = The desired lower water level at the inlet's location, based on the [[Lower threshold (Water Overlay)|LOWER_THRESHOLD]] of the inlet.
-* Q<sub>uth</sub> = The desired upper water level at the outlet's location, based on the outlet's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the inlet.
+* <math>Q_{uth}</math> = The desired upper water level at the outlet's location, based on the outlet's [[Upper threshold (Water Overlay)|UPPER_THRESHOLD]] of the inlet.
-* Q<sub>t</sub> = 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 Δt.
-* Q<sub>c</sub> = The total amount of water inflow (or outflow when negative) allowed based on the total capacity of the inlet.
+* <math>Q_c</math> = 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 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 amount of cells and cell size. Current implementation only has one cell.
-* Δw = The amount of water flow which takes place.
+* <math>\Delta w</math> = The amount of water flow which takes place.
 ==Related==

Inlet formula (Water Overlay): Difference between revisions

Revision as of 16:14, 4 December 2020

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