Weir formula (Water Overlay) - Revision history

Frank@tygron.nl at 11:47, 10 July 2026

2026-07-10T11:47:10Z

← Older revision		Revision as of 11:47, 10 July 2026
Line 70:		Line 70:

	* <math>z_{th}</math> = The height of the weir at time t, according to the height adjustment mechanism.		* <math>z_{th}</math> = The height of the weir at time t, according to the height adjustment mechanism.
	* <math>\tau_w</math> = The [[Weir target level (Water Overlay)\|WEIR_TARGET_LEVEL]] of ~~the~~ the weir.		* <math>\tau_w</math> = The [[Weir target level (Water Overlay)\|WEIR_TARGET_LEVEL]] of the weir.
	* <math>T_{wm}</math> = Moment in time in seconds after which the weir can adjust its height again.		* <math>T_{wm}</math> = Moment in time in seconds after which the weir can adjust its height again.
	* <math>z_{w,t}</math> = The [[Weir height (Water Overlay)\|WEIR_HEIGHT]] of the weir, at time <math>t</math>.		* <math>z_{w,t}</math> = The [[Weir height (Water Overlay)\|WEIR_HEIGHT]] of the weir, at time <math>t</math>.
Line 85:		Line 85:
	* <math>h_s</math> = The height of the water column relative to the top of the weir, on the side with the highest [[Surface water level formula (Water Overlay)\|water level]], at time <math>t</math>.		* <math>h_s</math> = The height of the water column relative to the top of the weir, on the side with the highest [[Surface water level formula (Water Overlay)\|water level]], at time <math>t</math>.
	* <math>h_d</math> = The height of the water column relative to the top of the weir, on the side with the lowest [[Surface water level formula (Water Overlay)\|water level]], at time <math>t</math>.		* <math>h_d</math> = The height of the water column relative to the top of the weir, on the side with the lowest [[Surface water level formula (Water Overlay)\|water level]], at time <math>t</math>.
	* <math>r_h</math> = The ratio of water heights on either side of the ~~culvert~~.		* <math>r_h</math> = The ratio of water heights on either side of the weir.
	* <math>Q</math> = The potential rate of water flow across the weir.		* <math>Q</math> = The potential rate of water flow across the weir.
	* <math>Q_f</math> = The potential rate of water flow across the weir, based on a free flow calculation.		* <math>Q_f</math> = The potential rate of water flow across the weir, based on a free flow calculation.
Line 142:		Line 142:
	}}		}}
	</references>		</references>
			\|api=*[[Api session event editor building set attribute]]
	}}		}}

	{{WaterOverlay formula nav}}		{{WaterOverlay formula nav}}

Frank@tygron.nl at 14:39, 8 July 2026

2026-07-08T14:39:20Z

← Older revision		Revision as of 14:39, 8 July 2026
Line 1:		Line 1:
	Flow across [[Weir (Water Overlay)\|weir]]s is calculated differently for free flow and submerged flow. ~~Optionally, the~~ height ~~of the weir can variate~~ based on a provided ~~height~~ values or an automatic adjustment~~. Therefore~~, we determined ~~the height of the weir~~ first.		Flow across [[Weir (Water Overlay)\|weir]]s is calculated differently for free flow and submerged flow. The weir height may vary based on provided values or automatic adjustment; therefore, it is determined first.

	First the upstream water level is calculated as followed:		First the upstream water level is calculated as followed:
Line 5:		Line 5:
	:<math>w_{u,t} = max( w_{l,t}, w_{r,t})</math>		:<math>w_{u,t} = max( w_{l,t}, w_{r,t})</math>

	Next, the adjusted weir height is determined. It either originates from the supplied weir height(s) <math>z_{w,t}</math> or it is adjusted according to the weir threshold level. ~~When it is~~ adjusted, a ~~moment in time~~ is set ~~for that weir,~~ during which it cannot ~~be adjusted~~.		Next, the adjusted weir height is determined. It either originates from the supplied weir height(s) <math>z_{w,t}</math> or it is adjusted according to the weir threshold level. Once adjusted, a lockout period is set during which the height cannot change again.

	:<math>z^{*}_{w,t} =		:<math>z^{*}_{w,t} =
Line 37:		Line 37:
	:<math>z_{w,t} = z^{*}_{w,t}</math>		:<math>z_{w,t} = z^{*}_{w,t}</math>

	~~Now knowing~~ the height ~~of the weir~~, the ~~height of the~~ water at ~~each end of the weir, relative to the weir, is~~ calculated:		With the weir height known, the relative water heights at both ends are calculated:
	: <math>h_s = max(0, max( w_{l,t}, w_{r,t} ) - z_{w,t})</math>		: <math>h_s = max(0, max( w_{l,t}, w_{r,t} ) - z_{w,t})</math>
	: <math>h_d = max(0, min( w_{l,t}, w_{r,t} ) - z_{w,t})</math>		: <math>h_d = max(0, min( w_{l,t}, w_{r,t} ) - z_{w,t})</math>


	~~Based on the relative water heights, the~~ weir uses either a submerged flow <math>Q_s</math> or a free flow <math>Q_f</math> formula, ~~based on~~ the following ratio:		The weir uses either a submerged flow <math>Q_s</math> or a free flow <math>Q_f</math> formula, determined by the following ratio:
	: <math>r_h = \frac{h_d}{h_s}</math>		: <math>r_h = \frac{h_d}{h_s}</math>
	:<math>		:<math>

Frank@tygron.nl: /* Free flow coefficients */

2025-11-14T12:54:04Z

Free flow coefficients

← Older revision		Revision as of 12:54, 14 November 2025
Line 111:		Line 111:
	* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.		* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.
	* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir, set to a default of 1.1		* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir, set to a default of 1.1
	* <math>N_w</math> = The [[Weir n (Water Overlay)\|WEIR_N]] of the weir, set to 3/2 by default.		* <math>N_w</math> = The [[Weir n (Water Overlay)\|WEIR_N]] of the weir, set to <math>\frac{3}{2}</math> by default.
	* <math>C_d</math> = Calculated Coefficient of discharge.		* <math>C_d</math> = Calculated Coefficient of discharge.
	* <math>g</math> = acceleration due to gravity.		* <math>g</math> = acceleration due to gravity.

Frank@tygron.nl: /* Free flow coefficients */

2025-11-14T12:53:34Z

Free flow coefficients

← Older revision		Revision as of 12:53, 14 November 2025
Line 106:		Line 106:
	:<math>f_{dw} \cdot C_w \approx C_d \cdot \sqrt{g}</math>		:<math>f_{dw} \cdot C_w \approx C_d \cdot \sqrt{g}</math>

	:<math>C_d=0,633 \cdot (1-\frac{0.0003}{h})^~~\frac~~{~~3}{2~~}</math>		:<math>C_d=0,633 \cdot (1-\frac{0.0003}{h})^{N_w}</math>

	where:		where:
	* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.		* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.
	* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir, set to a default of 1.1		* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir, set to a default of 1.1
			* <math>N_w</math> = The [[Weir n (Water Overlay)\|WEIR_N]] of the weir, set to 3/2 by default.
	* <math>C_d</math> = Calculated Coefficient of discharge.		* <math>C_d</math> = Calculated Coefficient of discharge.
	* <math>g</math> = acceleration due to gravity.		* <math>g</math> = acceleration due to gravity.

Frank@tygron.nl at 12:52, 14 November 2025

2025-11-14T12:52:17Z

← Older revision		Revision as of 12:52, 14 November 2025
Line 53:		Line 53:

	For free flow, it is calculated directly:		For free flow, it is calculated directly:
	: <math>Q_f = f_{dw} \cdot C_w \cdot b \cdot ( h_s - h_d )^{~~n_w~~}</math>		: <math>Q_f = f_{dw} \cdot C_w \cdot b \cdot ( h_s - h_d )^{N_w}</math>

	For submerged flow, the following calculation is used:		For submerged flow, the following calculation is used:
Line 91:		Line 91:
	* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.		* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.
	* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir.		* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir.
	* <math>~~n_w~~</math> = The [[Weir n (Water Overlay)\|WEIR_N]] of the weir.		* <math>N_w</math> = The [[Weir n (Water Overlay)\|WEIR_N]] of the weir.
	* <math>b</math> = The breadth of weir crest, adjustable using the [[Weir width (Water Overlay)\|WEIR_WIDTH]].		* <math>b</math> = The breadth of weir crest, adjustable using the [[Weir width (Water Overlay)\|WEIR_WIDTH]].
	* <math>f_{loss}</math> = Loss coefficient for submerged weirs, set to 0.9.		* <math>f_{loss}</math> = Loss coefficient for submerged weirs, set to 0.9.

Frank@tygron.nl at 12:51, 14 November 2025

2025-11-14T12:51:24Z

← Older revision		Revision as of 12:51, 14 November 2025
Line 53:		Line 53:

	For free flow, it is calculated directly:		For free flow, it is calculated directly:
	: <math>Q_f = f_{dw} \cdot C_w \cdot b \cdot ( h_s - h_d )^{~~3/2~~}</math>		: <math>Q_f = f_{dw} \cdot C_w \cdot b \cdot ( h_s - h_d )^{n_w}</math>

	For submerged flow, the following calculation is used:		For submerged flow, the following calculation is used:
Line 91:		Line 91:
	* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.		* <math>f_{dw}</math> = Dutch weir factor, set to 1.7.
	* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir.		* <math>C_w</math> = The [[Weir coefficient (Water Overlay)\|WEIR_COEFFICIENT]] of the weir.
			* <math>n_w</math> = The [[Weir n (Water Overlay)\|WEIR_N]] of the weir.
	* <math>b</math> = The breadth of weir crest, adjustable using the [[Weir width (Water Overlay)\|WEIR_WIDTH]].		* <math>b</math> = The breadth of weir crest, adjustable using the [[Weir width (Water Overlay)\|WEIR_WIDTH]].
	* <math>f_{loss}</math> = Loss coefficient for submerged weirs, set to 0.9.		* <math>f_{loss}</math> = Loss coefficient for submerged weirs, set to 0.9.

Frank@tygron.nl at 13:21, 5 March 2024

2024-03-05T13:21:10Z

← Older revision		Revision as of 13:21, 5 March 2024
Line 96:		Line 96:
	* <math>g</math> = {{gravity}}.		* <math>g</math> = {{gravity}}.
	* <math>\Delta w</math> = The water level change in meters, which takes place.		* <math>\Delta w</math> = The water level change in meters, which takes place.
	* <math>\Delta t</math> = Computational timestep in seconds.		* <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
	* <math>\Delta x</math> = Cell size in meters.		* <math>\Delta x</math> = Cell size in meters.

Frank@tygron.nl at 15:41, 25 January 2024

2024-01-25T15:41:27Z

← Older revision		Revision as of 15:41, 25 January 2024
Line 42:		Line 42:


	Based on the relative water heights, the weir uses either a submerged flow or a free flow formula, based on the following ratio:		Based on the relative water heights, the weir uses either a submerged flow <math>Q_s</math> or a free flow <math>Q_f</math> formula, based on the following ratio:
	: <math>r_h = \frac{h_d}{h_s}</math>		: <math>r_h = \frac{h_d}{h_s}</math>
	:<math>		:<math>

Frank@tygron.nl at 15:32, 25 January 2024

2024-01-25T15:32:18Z

← Older revision		Revision as of 15:32, 25 January 2024
Line 42:		Line 42:


	Based on the relative water heights, the weir ~~is judged to have~~ either a submerged flow or a free flow, based on the following ratio:		Based on the relative water heights, the weir uses either a submerged flow or a free flow formula, based on the following ratio:
	: <math>r_h = \frac{h_d}{h_s}</math>		: <math>r_h = \frac{h_d}{h_s}</math>
	:<math>		:<math>

Frank@tygron.nl at 15:10, 25 January 2024

2024-01-25T15:10:44Z

← Older revision		Revision as of 15:10, 25 January 2024
Line 9:		Line 9:
	:<math>z^{*}_{w,t} =		:<math>z^{*}_{w,t} =
	\begin{cases}		\begin{cases}
	z_{th}, & \text{if} & \\|{w_{u,t} - \tau_w}\\| > \mu \text{and} \tau_w > -10000 \\		z_{th}, & \text{if} & \\|{w_{u,t} - \tau_w}\\| > \mu \text{ and } \tau_w > -10000 \\
	z^{*}_{w,t-1}, & \text{if} & T_{wm} > T \\		z^{*}_{w,t-1}, & \text{if} & T_{wm} > T \\
	z_{w,t}, & \text{otherwise}		z_{w,t}, & \text{otherwise}