Pump formula (Water Overlay) - Revision history

Frank@tygron.nl at 13:13, 5 March 2024

2024-03-05T13:13:42Z

← Older revision		Revision as of 13:13, 5 March 2024
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	* <math>Q_{l,t}</math> = The desired amount of water at the entry based on the pump's [[Pump lower threshold (Water Overlay)\|LOWER_THRESHOLD]] attribute.		* <math>Q_{l,t}</math> = The desired amount of water at the entry based on the pump's [[Pump lower threshold (Water Overlay)\|LOWER_THRESHOLD]] attribute.
	* <math>Q_{u,t}</math> = The desired amount of water at the exit based on the pump's [[Pump upper threshold (Water Overlay)\|UPPER_THRESHOLD]] attribute.		* <math>Q_{u,t}</math> = The desired amount of water at the exit based on the pump's [[Pump upper threshold (Water Overlay)\|UPPER_THRESHOLD]] attribute.
	* <math>Q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] at timestep <math>\Delta t</math>, which is the amount of water the pump can possibly pump (or drain, when negative).		* <math>Q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] at time <math>t</math> for timestep <math>\Delta t</math>, which is the amount of water the pump can possibly pump (or drain, when negative).
	* <math>Q_c</math> = The maximum amount of water flow based on the total capacity of the pump.		* <math>Q_c</math> = The maximum amount of water flow based on the total capacity of the pump.
	* <math>A</math> = Size of the entry/exit area in <math>m^2</math>, based on the amount of cells and cell size. Current implementation only has one cell.		* <math>A</math> = Size of the entry/exit area in <math>m^2</math>, based on the amount of cells and cell size. Current implementation only has one cell.

Frank@tygron.nl at 13:10, 5 March 2024

2024-03-05T13:10:23Z

← Older revision		Revision as of 13:10, 5 March 2024
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	* <math>T_{u,t}</math> = The [[Pump upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.		* <math>T_{u,t}</math> = The [[Pump upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.
	* <math>q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] of the pump at time t.		* <math>q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] of the pump at time t.
	* <math>\Delta t</math> = Computational timestep.		* <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]].
	* <math>Q_{total}</math> = The pump capacity, defined in [[Inlet capacity (Water Overlay)\|INLET_CAPACITY]] of the pump.		* <math>Q_{total}</math> = The pump capacity, defined in [[Inlet capacity (Water Overlay)\|INLET_CAPACITY]] of the pump.
	* <math>Q_{0..n}</math> = The calculated previous amounts of flow.		* <math>Q_{0..n}</math> = The calculated previous amounts of flow.

Rudolf@tygron.nl at 12:42, 8 December 2020

2020-12-08T12:42:01Z

← Older revision		Revision as of 12:42, 8 December 2020
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	* <math>w_{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.		* <math>w_{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.
	* <math>w_{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.		* <math>w_{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.
	* <math>T_{l,t}</math> = The [[~~Lower~~ threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.		* <math>T_{l,t}</math> = The [[Pump lower threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.
	* <math>T_{u,t}</math> = The [[~~Upper~~ threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.		* <math>T_{u,t}</math> = The [[Pump upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.
	* <math>q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] of the pump at time t.		* <math>q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] of the pump at time t.
	* <math>\Delta t</math> = Computational timestep.		* <math>\Delta t</math> = Computational timestep.

Rudolf@tygron.nl at 12:41, 8 December 2020

2020-12-08T12:41:08Z

← Older revision		Revision as of 12:41, 8 December 2020
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	* <math>Q_{total}</math> = The pump capacity, defined in [[Inlet capacity (Water Overlay)\|INLET_CAPACITY]] of the pump.		* <math>Q_{total}</math> = The pump capacity, defined in [[Inlet capacity (Water Overlay)\|INLET_CAPACITY]] of the pump.
	* <math>Q_{0..n}</math> = The calculated previous amounts of flow.		* <math>Q_{0..n}</math> = The calculated previous amounts of flow.
	* <math>Q_{l,t}</math> = The desired amount of water at the entry based on the pump's [[~~Lower~~ threshold (Water Overlay)\|LOWER_THRESHOLD]] attribute.		* <math>Q_{l,t}</math> = The desired amount of water at the entry based on the pump's [[Pump lower threshold (Water Overlay)\|LOWER_THRESHOLD]] attribute.
	* <math>Q_{u,t}</math> = The desired amount of water at the exit based on the pump's [[~~Upper~~ threshold (Water Overlay)\|UPPER_THRESHOLD]] attribute.		* <math>Q_{u,t}</math> = The desired amount of water at the exit based on the pump's [[Pump upper threshold (Water Overlay)\|UPPER_THRESHOLD]] attribute.
	* <math>Q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] at timestep <math>\Delta t</math>, which is the amount of water the pump can possibly pump (or drain, when negative).		* <math>Q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] at timestep <math>\Delta t</math>, which is the amount of water the pump can possibly pump (or drain, when negative).
	* <math>Q_c</math> = The maximum amount of water flow based on the total capacity of the pump.		* <math>Q_c</math> = The maximum amount of water flow based on the total capacity of the pump.

Frank@tygron.nl at 15:50, 4 December 2020

2020-12-04T15:50:57Z

← Older revision		Revision as of 15:50, 4 December 2020
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	If a negative Pump q is defined:		If a negative Pump q is defined:
	: <math>Q_{p,t} = \Delta t \cdot q_t <\math>		: <math>Q_{p,t} = \Delta t \cdot q_t </math>

	If a lower threshold T<sub>l,t</sub> is defined as well:		If a lower threshold T<sub>l,t</sub> is defined as well:

Frank@tygron.nl at 15:50, 4 December 2020

2020-12-04T15:50:42Z

← Older revision		Revision as of 15:50, 4 December 2020
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	If a positive Pump q is defined:		If a positive Pump q is defined:
	: <math>Q_{p,t} = \Delta t \cdot q_t</math>		: <math>Q_{p,t} = \Delta t \cdot q_t </math>

	If a lower threshold T<sub>l,t</sub> is defined as well:		If a lower threshold T<sub>l,t</sub> is defined as well:
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	If a negative Pump q is defined:		If a negative Pump q is defined:
	: <math>Q_{p,t} = \Delta t * q_t<\math>		: <math>Q_{p,t} = \Delta t \cdot q_t <\math>

	If a lower threshold T<sub>l,t</sub> is defined as well:		If a lower threshold T<sub>l,t</sub> is defined as well:

Frank@tygron.nl at 15:50, 4 December 2020

2020-12-04T15:50:13Z

← Older revision		Revision as of 15:50, 4 December 2020
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	If an upper threshold T<sub>u,t</sub> is defined as well:		If an upper threshold T<sub>u,t</sub> is defined as well:
	: ~~''Q~~<~~sub~~>u,t~~</sub>~~ = min ( 0, ~~T<sub>~~u,t~~</sub>~~ - ~~w<sub>~~t,u</~~sub~~> ~~)''~~		: <math>Q_{u,t} = min ( 0, T_{u,t} - w_{t,u} )</math>

	If a capacity Q<sub>total</sub> is defined:		If a capacity Q<sub>total</sub> is defined:
	: ~~''Q~~<~~sub>c</sub~~> = ~~Q<sub>~~total~~</sub>~~ - abs ( ~~ΣQ<sub>~~0..t-1</~~sub~~> ~~)''~~		: <math>Q_c = Q_{total} - abs ( \sum_{0..t-1}Q_i )</math>

	After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.		After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.
	: ~~''Δw~~ = max( 0 , max( ~~Q<sub>~~l,t~~</sub>~~ , ~~Q<sub>~~u,t~~</sub>~~ , ~~Q<sub>t</sub>~~ , -~~Q<sub>c~~</~~sub~~> ~~) ) / A''~~		: <math>\Delta w = \frac { max( 0 , max( Q_{l,t} , Q_{u,t} , Q_t , -Q_c ) ) }{ A} </math>

	Where:		Where:

Frank@tygron.nl at 15:45, 4 December 2020

2020-12-04T15:45:32Z

← Older revision		Revision as of 15:45, 4 December 2020
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	After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.		After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.
	: ~~''Δw~~ = max( 0 , min( ~~Q<sub>~~l,t~~</sub>~~ , ~~Q<sub>~~u,t~~</sub>~~ , ~~Q<sub>~~t~~</sub>~~ , ~~Q<sub>~~c</~~sub~~> ~~) ) / A''~~		: <math>\Delta w = \frac {max( 0 , min( Q_{l,t} , Q_{u,t} , Q_{t} , Q_{c} ) ) }{A}</math>

	''Case 2: '''Draining''':''<br>		''Case 2: '''Draining''':''<br>
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	If a negative Pump q is defined:		If a negative Pump q is defined:
	: ~~''Q~~<~~sub~~>p,t~~</sub>~~ = Δt * ~~q<sub>t~~<~~/sub~~>''		: <math>Q_{p,t} = \Delta t * q_t<\math>

	If a lower threshold T<sub>l,t</sub> is defined as well:		If a lower threshold T<sub>l,t</sub> is defined as well:
	: ~~''Q~~<~~sub~~>l,t~~</sub>~~ = max ( 0, ~~w<sub>~~l,t~~</sub>~~ - ~~T<sub>~~l,t</~~sub~~> ~~)''~~		: <math>Q_{l,t} = max ( 0, w_{l,t} - T_{l,t} )</math>

	If an upper threshold T<sub>u,t</sub> is defined as well:		If an upper threshold T<sub>u,t</sub> is defined as well:

Frank@tygron.nl at 15:42, 4 December 2020

2020-12-04T15:42:02Z

← Older revision		Revision as of 15:42, 4 December 2020
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	The amount being pumped or drained is dependent on the water levels on both sides of the pump.		The amount being pumped or drained is dependent on the water levels on both sides of the pump.

	''Case 1: '''Pumping''':''~~<br>~~		''Case 1: '''Pumping''':''

	First the flow capacities are calculated.		First the flow capacities are calculated.

	If a positive Pump q is defined:		If a positive Pump q is defined:
	: ~~''Q~~<~~sub~~>p,t~~</sub>~~ = ~~Δt * q<sub>~~t</~~sub~~>''		: <math>Q_{p,t} = \Delta t \cdot q_t</math>

	If a lower threshold T<sub>l,t</sub> is defined as well:		If a lower threshold T<sub>l,t</sub> is defined as well:
	: ~~''Q~~<~~sub~~>l,t~~</sub>~~ = min ( 0, ~~w<sub>~~l,t~~</sub>~~ - ~~T<sub>~~l,t</~~sub~~> ~~)''~~		: <math>Q_{l,t} = min ( 0, w_{l,t} - T_{l,t} )</math>

	If an upper threshold ~~T<sub>~~u,t~~</sub>~~ is defined as well:		If an upper threshold T_{u,t} is defined as well:
	: ~~''Q~~<~~sub~~>u,t~~</sub>~~ = max ( 0, ~~T<sub>~~u,t~~</sub>~~- ~~w<sub>~~t,u</~~sub~~> ~~)''~~		: <math>Q_{u,t} = max ( 0, T_{u,t} - w_{t,u} )</math>

	If a capacity Q<sub>total</sub> is defined:		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 pumped upwards is calculated. If any of the terms are undefined, they are not included.		After calculating the capacities, the actual water pumped upwards is calculated. If any of the terms are undefined, they are not included.

Frank@tygron.nl at 15:33, 4 December 2020

2020-12-04T15:33:07Z

← Older revision		Revision as of 15:33, 4 December 2020
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	Where:		Where:
	* <math>w{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.		* <math>w_{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.
	* <math>w{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.		* <math>w_{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.
	* <math>T_{l,t}</math> = The [[Lower threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.		* <math>T_{l,t}</math> = The [[Lower threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.
	* <math>T_{u,t}</math> = The [[Upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.		* <math>T_{u,t}</math> = The [[Upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.

← Older revision		Revision as of 12:42, 8 December 2020
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	* <math>w_{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.		* <math>w_{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.
	* <math>w_{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.		* <math>w_{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.
	* <math>T_{l,t}</math> = The [[~~Lower~~ threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.		* <math>T_{l,t}</math> = The [[Pump lower threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.
	* <math>T_{u,t}</math> = The [[~~Upper~~ threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.		* <math>T_{u,t}</math> = The [[Pump upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.
	* <math>q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] of the pump at time t.		* <math>q_t</math> = The [[Pump q (Water Overlay)\|PUMP_Q]] of the pump at time t.
	* <math>\Delta t</math> = Computational timestep.		* <math>\Delta t</math> = Computational timestep.

← Older revision		Revision as of 15:33, 4 December 2020
Line 44:		Line 44:

	Where:		Where:
	* <math>w{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.		* <math>w_{t,l}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the lower water level entry at time t, relative to {{datum}}.
	* <math>w{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.		* <math>w_{t,u}</math> = The [[Surface water level formula (Water Overlay)\|water level]] at the upper water level entry at time t, relative to {{datum}}.
	* <math>T_{l,t}</math> = The [[Lower threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.		* <math>T_{l,t}</math> = The [[Lower threshold (Water Overlay)\|LOWER_THRESHOLD]] of the pump at time t.
	* <math>T_{u,t}</math> = The [[Upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.		* <math>T_{u,t}</math> = The [[Upper threshold (Water Overlay)\|UPPER_THRESHOLD]] of the pump at time t.