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The information on this was extracted from Practical hydraulics by Melvyn Kay, published in 1998 by E & FN Spon.
It explains very nicely the fundamental aspects of broad crested weirs with some very clear diagrams.
These are much more robust than sharp-crested weirs and are used extensively for , flow measurement and water level regulation in rivers and canals (Figure 7.5a below).
Height of weir and critical flow
All solid weirs work on the principle that the flow over the weir must go through the critical depth. It is the height of a weir that determines whether or not the flow goes critical. Once this happens a formula for discharge can be developed using the concept of specific energy and the special conditions that occur at the critical point.
The following formula links the channel discharge (Q) with the upstream water depth measured above the weir crest (H):
Q = CLH1.5
where C is the weir coefficient, L is length of the weir crest (m) and H is head on the weir measured from the crest (m). To see how this formula is developed you need to refer to the lab experiment page on broad crested weirs. As there is some draw-down close to the weir, the head is usually measured a few metres upstream where the water level is unaffected by the weir.
Note that strictly speaking H is the measurement from the weir crest to the energy line as it includes the kinetic energy term. In practice H is measured from the weir crest to the water surface. The error involved in this is relatively small and can be taken into account in the value of the weir coefficient C. Alternatively, the head H is measured in a stilling chamber by the side of the channel where the kinetic energy has been dissipated.
As the formula is based on critical depth it is not dependent on the shape of the weir. So the same formula can be used for any critical depth weir and not just for broad crested weirs. Only the value of C changes to take account of the different weir, shapes. See the diagrams below.
Determining the height of a weir
Just how high a weir must be for the flow to go critical is determined from the specific energy diagram. The effect of constructing a weir in a channel is the same as building a step up on the bed. In the case of a step up, the depth of water on the step decreases and the velocity increases (Figure 7.6a, see below). A worked example would show that for a O.3m high step up, the depth of water was reduced from 0.99m upstream to 0.67m on the step (this is summarised in Figure 7.6b). This is still well above the critical depth of 0.29m.
Now assume that the step up on the bed is a weir and the intention is to make the flow go critical on the weir crest. This can be achieved by raising the crest level. Raising it from O.3m to O.56m further reduces the depth on the weir from 0.67m to 0.29m, which is the critical depth (Figure 7.6c. This is the minimum weir height required for critical flow. Note that although the weir height has increased by 0.26m, the upstream depth remains unchanged at 0.99m. If the weir height is increased beyond 0.56m the flow will still go critical on the crest and remain at the critical depth of 0.29m. It will not and cannot fall below this value. The difference will be in the upstream water level which will now rise. Remember there is a unique relationship between the head on a weir and the discharge. So if the weir is raised by a further 0.1m to 0.66m the upstream water level will also be raised by 0.lm to maintain the correct head on the weir (Figure 7.6d).
The operation of weirs is often misunderstood and it is believed that they cause the flow to back up and so raise water levels upstream. This only happens once critical conditions are achieved on the weir. When a weir is too low for critical flow it is the water level on the weir that drops. The upstream level is unaffected. But once critical flow is achieved, raising the weir more than is necessary will have a direct effect on the upstream water level.
Being sure of critical flow
Critical flow must occur for the discharge formula to work. But in practice it is not always possible to see critical flow and so some detective work is needed. Figure 7.7, below, shows the changing flow conditions as water flows over a weir. Upstream the flow is sub-critical, it then goes critical over the weir and then super-critical downstream. It changes back to sub-critical through a hydraulic jump. When this sequence of changes occurs it can be reasoned that critical flow must have occurred and so the weir is working properly. The changes are best verified in reverse from the downstream side. Remember a hydraulic jump can only form when the flow is super-critical and so if there is a hydraulic jump in the downstream channel, the flow over the weir must be super-critical. If the upstream flow is sub-critical, which can be verified by the water surface dropping as water flows over the weir, then somewhere in between the flow must have gone critical. So a hydraulic jump downstream is good evidence that critical flow has occurred.
Note that it is not important to know exactly where critical flow occurs. It is enough just to know that it has occurred for the formula to work. In the laboratory, the depth of flow above the weir can be measured so that critical depth flow can be determined.
Broad-crested weirs are very common structures used for flow measurement. They have a broad rectangular shape with a level crest rounded at the edge (Figure 7.5b). The value of C for a broad-crested weir is 1.6 and so the formula becomes:
Q = 1.6LH1.5
The formula derived from the total energy equation (Bernoulli equation) is:
Q = 1.705LH1.5
So the coefficient of discharge determined in the laboratory from
should be around 0.94 as long as critical depth flow has occurred.
One disadvantage of this weir is the region of dead water just upstream. Silt and debris can accumulate here and this can seriously reduce the accuracy of the weir formula. Another is the head loss between the upstream and downstream levels. Whenever a weir (or a flume) is installed in a channel there is always a loss of energy particularly if there is a hydraulic jump downstream. This is the hydraulic price to be paid for measuring the flow.
Crump weirs are commonly used in the UK for discharge measurement in rivers. Like the broad-crested weir it relies on critical conditions occurring for the discharge formula to work. It has a triangular shaped section (Figure 7.5c near the top of the page). The upstream slope is 1 in 2 and the downstream is 1 in 5. The sloping upstream face helps to reduce the dead water region that occurs with broad-crested weirs. It can also tolerate a high level of submergence. Its crest can also be constructed in a vee shape so that it can be used accurately for both small and large discharges.
Last Edited : 22 January 2011 14:26:17