Drainage formula (Water Overlay) - Revision history

Frank@tygron.nl at 13:08, 5 March 2024

2024-03-05T13:08:03Z

Frank@tygron.nl at 16:06, 26 January 2024

2024-01-26T16:06:26Z

← Older revision		Revision as of 16:06, 26 January 2024
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	; Models		; Models
	: [[Surface model (Water Overlay)]]		: [[Surface model (Water Overlay)]]
	: [[~~Underground~~ model (Water Overlay)]]		: [[Ground model (Water Overlay)]]
	}}		}}
	{{WaterOverlay formula nav}}		{{WaterOverlay formula nav}}

Frank@tygron.nl: /* Drainage passive */

2021-05-07T16:06:28Z

Drainage passive

← Older revision		Revision as of 16:06, 7 May 2021
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	<math>Q_d = A_d \cdot (w_d - z_d) \cdot f_s</math>		<math>Q_d = A_d \cdot (w_d - z_d) \cdot f_s</math>

	<math>Q_t = min ( Q_p, Q_b , ~~Q_w~~ )</math>		<math>Q_t = min ( Q_p, Q_b , Q_d )</math>

	else:		else:
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	<math>Q_w = A_w \cdot (w_w - z_w) </math>		<math>Q_w = A_w \cdot (w_w - z_w) </math>

	<math>Q_t = min ( Q_p, Q_b , ~~Q_d~~ )</math>		<math>Q_t = min ( Q_p, Q_b , Q_w )</math>

	Where:		Where:

Frank@tygron.nl at 16:05, 7 May 2021

2021-05-07T16:05:49Z

← Older revision		Revision as of 16:05, 7 May 2021
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	: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.		: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.
	: <math>\Delta t</math> is the computational timestep.		: <math>\Delta t</math> is the computational timestep.
	~~: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.~~
	: <math>w_d</math> is the ground water level, above the drainage, in meters.		: <math>w_d</math> is the ground water level, above the drainage, in meters.
	: <math>w_w</math> is the water level in the waterway.		: <math>w_w</math> is the water level in the waterway.
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	: <math>A_w</math> is the waterway area size in square meters.		: <math>A_w</math> is the waterway area size in square meters.
	: <math>f_s</math> is the average storage percentage of the ground above the drainage.		: <math>f_s</math> is the average storage percentage of the ground above the drainage.
			: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.
	: <math>Q_b</math> is the amount transferred for a balanced ground and surface water level.		: <math>Q_b</math> is the amount transferred for a balanced ground and surface water level.
	: <math>Q_d</math> is the amount of water available in the ground above the drainage.		: <math>Q_d</math> is the amount of water available in the ground above the drainage.

Frank@tygron.nl at 16:05, 7 May 2021

2021-05-07T16:05:26Z

← Older revision		Revision as of 16:05, 7 May 2021
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	: <math>w_w</math> is the water level in the waterway.		: <math>w_w</math> is the water level in the waterway.
	: <math>z_d</math> is the drainage datum height in meters.		: <math>z_d</math> is the drainage datum height in meters.
			: <math>z_w</math> is the max waterway height.
	: <math>A_d</math> is the drainage area size in square meters.		: <math>A_d</math> is the drainage area size in square meters.
	: <math>A_w</math> is the waterway area size in square meters.		: <math>A_w</math> is the waterway area size in square meters.
	~~: <math>z_w</math> is the max waterway height.~~
	: <math>f_s</math> is the average storage percentage of the ground above the drainage.		: <math>f_s</math> is the average storage percentage of the ground above the drainage.
	: <math>Q_b</math> is the amount transferred for a balanced ground and surface water level.		: <math>Q_b</math> is the amount transferred for a balanced ground and surface water level.

Frank@tygron.nl at 16:04, 7 May 2021

2021-05-07T16:04:45Z

← Older revision		Revision as of 16:04, 7 May 2021
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	: <math>Q_d</math> is the amount of water available in the ground above the drainage.		: <math>Q_d</math> is the amount of water available in the ground above the drainage.
	: <math>Q_w</math> is the amount of water available in the waterway.		: <math>Q_w</math> is the amount of water available in the waterway.
	: <math>Q_t</math> is the actual drained, or ~~pumped~~ backwards, volume at time t.		: <math>Q_t</math> is the actual drained, or infiltrated backwards, volume at time t.

	==Drainage active==		==Drainage active==

Frank@tygron.nl: /* Drainage passive */

2021-05-07T16:03:57Z

Drainage passive

← Older revision		Revision as of 16:03, 7 May 2021
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	First the flow capacity is calculated		First the flow capacity is calculated

	<math>~~Q_{p,t}~~=\Delta t \cdot q_t</math>		<math>Q_p=\Delta t \cdot q_t</math>

	<math>~~Q_{b}~~ = A_d \cdot f_s \cdot \frac{\|\|w_d - w_w\|\| \cdot A_w}{A_d \cdot f_s + A_w}</math>		<math>Q_b = A_d \cdot f_s \cdot \frac{\|\|w_d - w_w\|\| \cdot A_w}{A_d \cdot f_s + A_w}</math>

	if <math>w_w ~~> w_d~~</math> then:		if <math>w_d > w_w</math> then:

	<math>~~Q_{max}~~ = ~~A_w~~ \cdot (~~w_w~~ - ~~z_w~~) </math>		<math>Q_d = A_d \cdot (w_d - z_d) \cdot f_s</math>

			<math>Q_t = min ( Q_p, Q_b , Q_w )</math>

	else:		else:

	<math>~~Q_{max}~~ = ~~A_d~~ \cdot (~~w_d~~ - ~~z_d) \cdot f_s</math>~~		<math>Q_w = A_w \cdot (w_w - z_w) </math>

	~~<math>Q_{d} = min ( Q_{p,t}, Q_{b} , Q_{max}~~ )</math>

			<math>Q_t = min ( Q_p, Q_b , Q_d )</math>

	Where:		Where:
	: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.		: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.
	: <math>\Delta t</math> is the computational timestep.		: <math>\Delta t</math> is the computational timestep.
	: <math>~~Q_{p,t}~~</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.		: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.
	: <math>w_d</math> is the ground water level, above the drainage, in meters.		: <math>w_d</math> is the ground water level, above the drainage, in meters.
	: <math>w_w</math> is the water level in the waterway.		: <math>w_w</math> is the water level in the waterway.
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	: <math>z_w</math> is the max waterway height.		: <math>z_w</math> is the max waterway height.
	: <math>f_s</math> is the average storage percentage of the ground above the drainage.		: <math>f_s</math> is the average storage percentage of the ground above the drainage.
	: <math>~~Q_{b}~~</math> is the amount transferred for a balanced ground and surface water level.		: <math>Q_b</math> is the amount transferred for a balanced ground and surface water level.
	: <math>~~Q_{max}~~</math> is the amount of water available in the ground above the drainage.		: <math>Q_d</math> is the amount of water available in the ground above the drainage.
	: <math>~~Q_{d}~~</math> is the actual drained volume at time t.		: <math>Q_w</math> is the amount of water available in the waterway.
			: <math>Q_t</math> is the actual drained, or pumped backwards, volume at time t.

	==Drainage active==		==Drainage active==

Frank@tygron.nl: /* Drainage active */

2021-05-07T15:59:24Z

Drainage active

← Older revision		Revision as of 15:59, 7 May 2021
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	: <math>T_{o,t}</math> is the overflow threshold in meters at time t.		: <math>T_{o,t}</math> is the overflow threshold in meters at time t.
	: <math>Q_o</math> is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.		: <math>Q_o</math> is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.
	: <math>Q_w</math> is the amount of water available in the ~~water way, above the overflow threshold~~.		: <math>Q_w</math> is the amount of water available in the waterway.
	: <math>Q_{t}</math> is the actual drained (or pumped) volume at time t.		: <math>Q_{t}</math> is the actual drained (or pumped) volume at time t.

Frank@tygron.nl: /* Drainage active */

2021-05-07T15:57:33Z

Drainage active

← Older revision		Revision as of 15:57, 7 May 2021
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	: <math>w_w</math> is the water level in the waterway.		: <math>w_w</math> is the water level in the waterway.
	: <math>z_d</math> is the drainage datum height in meters.		: <math>z_d</math> is the drainage datum height in meters.
			: <math>z_w</math> is the waterway's datum height.
	: <math>f_s</math> is the average storage percentage of the ground above the drainage.		: <math>f_s</math> is the average storage percentage of the ground above the drainage.
	: <math>Q_d</math> is the amount of water available in the ground above the drainage.		: <math>Q_d</math> is the amount of water available in the ground above the drainage.
	: <math>T_{o,t}</math> is the overflow threshold in meters at time t.		: <math>T_{o,t}</math> is the overflow threshold in meters at time t.
	: <math>Q_o</math> is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.		: <math>Q_o</math> is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.
	: <math>~~z_w~~</math> is the ~~waterway's datum height~~.		: <math>Q_w</math> is the amount of water available in the water way, above the overflow threshold.
	: <math>Q_{t}</math> is the actual drained (or pumped) volume at time t.		: <math>Q_{t}</math> is the actual drained (or pumped) volume at time t.

Frank@tygron.nl: /* Drainage active */

2021-05-07T15:55:43Z

Drainage active

← Older revision		Revision as of 15:55, 7 May 2021
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	If a positive [[Drainage q (Water Overlay)\|DRAINAGE_Q]] is defined:		If a positive [[Drainage q (Water Overlay)\|DRAINAGE_Q]] is defined:
	: <math>~~Q_{p,t}~~ = \Delta t \cdot q_t </math>		: <math>Q_p = \Delta t \cdot q_t </math>
	: <math>~~Q_{g,t}~~ = (w_d - z_d)\cdot f_s</math>		: <math>Q_d = (w_d - z_d)\cdot f_s</math>

	If an overflow threshold <math>T_{o,t}</math> is defined as well:		If an overflow threshold <math>T_{o,t}</math> is defined as well:
	: <math>~~Q_{o,t}~~ = max ( 0, T_{o,t} - w_w )</math>		: <math>Q_o = max ( 0, T_{o,t} - w_w )</math>

	The actual water pumped out of the drainage system is calculated. If any of the terms are undefined, they are not included.		The actual water pumped out of the drainage system is calculated. If any of the terms are undefined, they are not included.
	: <math>Q_t = max( 0 , min( Q_{~~g,t~~} , Q_{o,t} , Q_{p,t}))</math>		: <math>Q_t = max( 0 , min( Q_{d} , Q_{o} , Q_{p}))</math>

	''Case 2: '''Active Reverse Draining''':''<br>		''Case 2: '''Active Reverse Draining''':''<br>

	If a negative [[Drainage q (Water Overlay)\|DRAINAGE_Q]] is defined:		If a negative [[Drainage q (Water Overlay)\|DRAINAGE_Q]] is defined:
	: <math>~~Q_{p,t}~~ = \Delta t \cdot q_t </math>		: <math>Q_p = \Delta t \cdot q_t </math>
	: <math>~~Q_{w,t}~~ = min ( 0, z_w - w_{t,w} )</math>		: <math>Q_w = min ( 0, z_w - w_{t,w} )</math>

	If an overflow threshold <math>T_{o,t}</math> is defined as well:		If an overflow threshold <math>T_{o,t}</math> is defined as well:
	: <math>~~Q_{o,t}~~ = min ( 0, T_{o,t} - w_{t,w} )</math>		: <math>Q_o = min ( 0, T_{o,t} - w_{t,w} )</math>

	The actual water pumped into the drainage system is calculated. If any of the terms are undefined, they are not included.		The actual water pumped into the drainage system is calculated. If any of the terms are undefined, they are not included.
	: <math>Q_t = max( 0 , max( ~~Q_{p~~,t} , ~~Q_{w,t} , Q_{o,t}~~) ) </math>		: <math>Q_t = max( 0 , max( Q_p, Q_w , Q_o) ) </math>


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	: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.		: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.
	: <math>\Delta t</math> is the computational timestep.		: <math>\Delta t</math> is the computational timestep.
	: <math>~~Q_{p,t}~~</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.		: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.
	: <math>w_d</math> is the ground water level, above the drainage, in meters.		: <math>w_d</math> is the ground water level, above the drainage, in meters.
	: <math>w_w</math> is the water level in the waterway.		: <math>w_w</math> is the water level in the waterway.
	: <math>z_d</math> is the drainage datum height in meters.		: <math>z_d</math> is the drainage datum height in meters.
	~~: <math>A_d</math> is the drainage area size in square meters.~~
	~~: <math>A_w</math> is the waterway area size in square meters.~~
	~~: <math>z_w</math> is the max waterway height.~~
	: <math>f_s</math> is the average storage percentage of the ground above the drainage.		: <math>f_s</math> is the average storage percentage of the ground above the drainage.
	: <math>~~Q_{b}~~</math> is the amount ~~transferred for a balanced~~ ground ~~and surface water level~~.		: <math>Q_d</math> is the amount of water available in the ground above the drainage.
	: <math>Q_{~~max~~}</math> is the amount ~~available in~~ the ~~ground above~~ the ~~drainage~~.		: <math>T_{o,t}</math> is the overflow threshold in meters at time t.
	: <math>Q_{d}</math> is the actual drained volume at time t		: <math>Q_o</math> is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.
			: <math>z_w</math> is the waterway's datum height.
			: <math>Q_{t}</math> is the actual drained (or pumped) volume at time t.

	{{article end		{{article end

← Older revision		Revision as of 13:08, 5 March 2024
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	Where:		Where:
	: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.		: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.
	: <math>\Delta t</math> is the computational timestep.		: <math>\Delta t</math> is the computational [[Timestep formula (Water Overlay)\|timestep]].
	: <math>w_d</math> is the ground water level, above the drainage, in meters.		: <math>w_d</math> is the ground water level, above the drainage, in meters.
	: <math>w_w</math> is the water level in the waterway.		: <math>w_w</math> is the water level in the waterway.
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	: <math>A_w</math> is the waterway area size in square meters.		: <math>A_w</math> is the waterway area size in square meters.
	: <math>f_s</math> is the average storage percentage of the ground above the drainage.		: <math>f_s</math> is the average storage percentage of the ground above the drainage.
	: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.		: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep <math>\Delta t</math>.
	: <math>Q_b</math> is the amount transferred for a balanced ground and surface water level.		: <math>Q_b</math> is the amount transferred for a balanced ground and surface water level.
	: <math>Q_d</math> is the amount of water available in the ground above the drainage.		: <math>Q_d</math> is the amount of water available in the ground above the drainage.
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	Where:		Where:
	: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.		: <math>q_t</math> is the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} at time t.
	: <math>\Delta t</math> is the computational timestep.		: <math>\Delta t</math> is the computational [[Timestep formula (Water Overlay)\|timestep]].
	: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep Δt.		: <math>Q_p</math> is the possible amount of water drained, or pumped back when negative, based on the [[Drainage q (Water Overlay)\|DRAINAGE_Q]] of the {{Drainage}} and timestep <math<\Delta t</math>.
	: <math>w_d</math> is the ground water level, above the drainage, in meters.		: <math>w_d</math> is the ground water level, above the drainage, in meters.
	: <math>w_w</math> is the water level in the waterway.		: <math>w_w</math> is the water level in the waterway.