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Common weir constructions are the rectangular weir, the triangular or v-notch weir, and the broad-crested weir. Weirs are called sharp-crested if their crests are constructed of thin metal plates, and broad-crested if they are made of wide timber or concrete.

Water level-discharge relationships can be applied and meet accuracy requirements for sharp-crested weirs if the installation is designed and installed consistent with established ASTM and ISO standards.

Rectangular weirs and triangular or v-notch weirs are often used in water supply, wastewater and sewage systems. They consist of a sharp edged plate with a rectangular, triangular or v-notch profile for the water flow.

Broad-crested weirs can be observed in dam spillways where the broad edge is beneath the water surface across the entire stream. Flow measurement installations with broad-crested weirs will meet accuracy requirements only if they are calibrated.

Other available weirs are the trapezoidal (Cipolletti) weir, Sutro (proportional) weir and compound weirs (combination of the previously mentioned weir shapes).

The flow rate measurement in a rectangular weir is based on the Bernoulli Equation principles and can be expressed as:

Flow through a rectangular weir can be expressed in imperial units with the Francis formula

For a triangular or v-notch weir the flow rate can be expressed as:

For the broad-crested weir the flow rate can be expressed as:

For measuring the flow rate it's obviously necessary to measure the flow levels, then use the equations above for calculating. It's common to measure the levels with:

· ultrasonic level transmitters, or

· pressure transmitters

Ultrasonic level transmitters are positioned above the flow without any direct contact with the flow. Ultrasonic level transmitters can be used for all measurements. Some of the transmitters can even calculate a linear flow signal - like a pulse signal or *4 - 20 mA* signal - before transmitting it to the control system.

Pressure transmitters can be used for the sharp-crested weirs and for the first measure point in broad-crested weir. The pressure transmitter outputs a linear level signal - *4 - 20 mA* - and the flow must in general be calculated in the control system.

To determine the relationship between upstream head and flow-rate for water flowing over a Broad Crested weir (long base weir), to calculate the discharge coefficient and to observe the flow patterns obtained.

Broad crested weirs are robust structures that are generally constructed from reinforced concrete and which usually span the full width of the channel. They are used to measure the discharge of rivers, and are much more suited for this purpose than the relatively flimsy sharp crested weirs. Additionally, by virtue of being a critical depth meter, the broad crested weir has the advantage that it operates effectively with higher downstream water levels than a sharp crested weir.

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Only rectangular broad crested weirs will be considered, although there are a variety of possible shapes: triangular, trapezoidal and round crested all being quite common. If a standard shape is used then there is a large body of literature available relating to their design, operation, calibration and coefficient of discharge (see BS3680). However, if a unique design is adopted, then it will have to be calibrated either in the field by river gauging or by means of a scaled-down model in the laboratory.

A rectangular broad crested weir is shown above. When the length, *L, *of the crest is greater than about three times the upstream head, the weir is broad enough for the flow to pass through critical depth somewhere near to its downstream edge. Consequently this makes the calculation of* *the discharge relatively straightforward. Applying the continuity equation to the section on the weir crest where the flow is at critical depth gives:

Now assuming that the breadth of* *the weir *(b)* spans the full width *(B) *of* *the channel and that the cross-sectional area of* *flow is rectangular, then:

Ac = *b *x* Dc* and *Vc *= (*g** *x *Dc*)^{1/2} (See your notes regarding Froude No.)

Thus from the continuity equation,

However, equation 1 does not provide a very practical means of* *calculating *Q. * It is much easier to use a stilling well located in a gauging hut just upstream of* *the weir to measure the head of water, *H*_{1}, above the crest than to attempt to measure the critical depth on the crest itself. In order to eliminate *Dc *from the equation, we can use the fact that in a rectangular channel . Using the weir crest as the datum level, and assuming no loss of energy, the specific energy at an upstream section (subscript 1**,**** **Fig. above) equals that at the critical section:

If you substitute this expression into Eqn 1, it gives:

The term in the above equation is the velocity head of the approaching flow. As with the rectangular sharp crested weir, the problem arises that the velocity of approach,*V*_{1}* *cannot be calculated until Q is known, and Q cannot be calculated until *V*_{1} is known. A way around this is to involve an iterative procedure, but in practice it is often found that the velocity head is so small as to be negligible. Alternatively, a coefficient of discharge, *C*, can be introduced into the equation to allow for the velocity of approach, non-parallel streamlines over the crest, and energy losses. *C* varies between about 1.4 and 2.1 according to the shape of the weir and the discharge, but frequently has a value of about 1.6. Thus:

The broad crested weir will cease to operate according to the above equations if a backwater from further downstream causes the weir to submerge. Equations 2 and 3 can be applied until the head of water above the crest on the downstream side of the weir, *H*_{D}, exceeds the critical depth on the crest. This is often expressed as the submergence ratio, *H*_{D}/H_{1. }_{ }The weir will operate satisfactorily up to a submergence ratio of about 0.66, that is when *H*_{D} = *0.66H*_{1}. For sharp crested weirs the head-discharge relationship becomes inaccurate at a submergence ratio of around 0.22, so the broad crested type has a wider operating range. Once the weir has submerged, the downstream water level must also be measured and the discharge calculated using a combination of weir and orifice equations. However, this requires the evaluation of two coefficients of discharge, which means that the weir must be calibrated by river gauging during high flows. This can be accomplished using a propeller type velocity (current) meter.

A common mistake made by many students in design classes is to calculate the head that will occur over a weir at a particular discharge without considering at all the height of weir required to obtain critical depth on the crest. For example, suppose the depth of flow approaching the weir is 2 m. If the height, *p, *of the weir crest above the bottom of the channel is only 50 mm, the weir is so low that the flow would be totally unaffected by it and certainly would not be induced to pass through critical depth. Equally ridiculously, if the weir is 4 m high it would behave as a small dam and would raise the upstream water level very considerably and cause quite serious flooding.

So how can we work out the optimum height for the weir? What height will give supercritical flow without unduly raising the upstream water level?

The answer is obtained by applying the energy equation to two sections (See diagram below). One some distance upstream of the weir (subscript 1) and the second on the weir crest where critical depth occurs (subscript c). In this case the bottom of the channel is used as the datum level. Assuming that the channel is horizontal over this relatively short distance, that both cross-sectional areas of flow are rectangular, and that there is no loss of energy, then:

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This is usually sufficient to enable equation 4 to be solved for *p *when *Q *and *D*_{1} are known. Alternatively, the depth, *D*_{1}, upstream of the weir can be calculated if *Q *and *p *are known. When calculating the 'ideal' height of weir, it must be appreciated that it is only ideal for the design discharge. The weir cannot adjust its height to suit the flow, so at low flows it may be too high, and at high flows it may be too low. Consequently 'V' shaped concrete weirs are often used, or compound crump weirs that have crests set at different levels.

1. Multi-Purpose Teaching Flume (Arm field C4)

2. Broad Crested Weir

3. Hook and point gauge, 300mm scale,- 2 required

4. Stopwatch if measuring flow rate using the volumetric tank

1. Before the experiment has been started, the apparatus has been ensured that in horizontal position.

2. The model of broad crested weir has been put and been screwed it to the equipments. The supply valve has been opened until the water flows to upper level weir.

3. After the stable flow has been reached, the measure gauge has been used to obtained the d_{u} and d_{c} value. The discharge, value of this flow has been determined.

4. The flow rate has been change in order to get more values of Q, d_{u} and d_{c}.

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