4.34. Vee notch Weir

4.34.1. V-weir (class)

Fig. 4.34.1 Thin plate weir with one or more triangular shaped notches

Fall type

type label	Description	active
Vee notch Weir	Thin plate weir with one or more Vee shaped notches, according to ISO 1438/1 1980(E)	no

4.34.1.1. Mathematical model

The Vee notch weir is a short, sharp weir with one or more Vee shaped notches. The model can be used for a Vee shaped measuring weir or a Vee shaped weir of a tank.

A precondition is that the upstream fluid level is always in the V-shape and the weir discharge is independent of the downstream fluid level. So, the downstream fluid level should always below the bottom of the Vee shaped weir.

The weir discharge per Vee shape is determined by:

(4.34.1)\[Q=C_{D} \frac{8}{15} \sqrt{2 g} \tan \left(\frac{\theta}{2}\right) h_{v}^{\frac{5}{2}}\]

(4.34.2)\[F_{1}: Q_{t o t}=N_{v} Q\]

Fig. 4.34.2 Defenition sketch of the Vee notch weir

with:

Symbol	Unit	description
Q	m3/s	Discharge per V shape
CD	-	Discharge coefficient, depended on the shape of the weir.
g	m2/s	Gravitational acceleration
\(\theta\)	˚	total V angle
hv	m	Upstream fluid level, relative to bottom of V
hb	m	Bottom level of V shape relative to reference plane
ht	m	Top level of V shape relative to reference plane
Nv	-	Number of V’s
Qtot	m3/s	Total weir discharge

The level of the top (h_t) and bottom (h_b) of the Vee notch are given relative to the reference plane.

If the upstream fluid level is above the top of the V shape (h₁>h_t), water flows over the whole edge. There is no critical flow anymore when the downstream fluid level is above the bottom of the V shape (h₂>h_b). In both cases the programme gives an error because you are outside the range of the discharge equation.

The weir is dry when the upstream fluid level drops below the bottom of the V (h₁<h_b). In this case:

(4.34.3)\[F_{1}: Q=0\]

The storage upstream of the weir is no part of the Vee notch weir component and should be modelled with another component (SURGTW).

4.34.2. Vee notch Weir

4.34.2.1. Hydraulic specifications

Description	Input	Unit	Range	default	Remarks
bottom V-shape	Real	[m]	(-100 ; 10000]		Downstream fluid level should be below bottom of V-shape
top level V-shape	Real	[m]	(-100; 10000]		Upstream fluid level should be below top of V-shape
Discharge coefficient	Real	[-]	(0, 1]	0,578	This is a mean value from the standard
V-shape angle	Real	[˚]	(20; 100]	60	See standard
Number of V’s	Integer	[-]	(1, 1000]	1
Initial status			critical / dry	critical

See also “Mathematical model” on page 461.

4.34.2.2. Component specific output

None

4.34.2.3. H-action

None

4.34.2.4. Component messages

Message	explanation
Starts in critical state	Informative: Upstream fluid level is above the bottom of the V-shape in steady state. Q>0.
Starts in closed state.	Informative: Upstream fluid level is below the bottom of the V-shape in steady state. Q=0.
Closes	Informative, weir becomes dry.
Enters critical state	Informative: Upstream fluid level becomes larger than bottom of V-shape. Q>0
Error: upstream level above top V-notch. Calculation is no longer valid	Upstream level becomes larger than top of V-shaped notch. The calculated discharge is not correct anymore.
Error: Return flow not allowed	Downstream fluid level is larger than upstream fluid level; discharge in opposite direction is not allowed.

4.34.2.5. Example

The following example demonstrates how to model a settling tank for sewage treatment works.

Fig. 4.34.3 Schematic Wanda model of a settling tank for a sewage treatment plant.