The broad-crested weir.

If an obstruction is to be built across a river and there is a good reason to want to measure the flow, the flow measurement device and the obstruction may as well be one device. The broad-crested weir is an adaptation of a wall for the measurement of flow.

 

In order to understand the broad-crested weir let us investigate the physics of a specially shaped wall across a rectangular channel. The wall is shown in figure 10-24. The front is radiused to produce acceptably smooth flow over the top of the wall that may be flat and level or angled downwards to give a slope. The wall has a square downstream edge. There is nothing that is adjustable in a broad-crested weir and the profile of water flowing over the weir depends mainly on the upstream depth unless the whole thing is submerged by exceptional conditions downstream. In figure 10-24 I have drawn several profiles for the water for different upstream depths and it is immediately obvious that there will be very different profiles for the case when the upstream depth is so low that the water only just flows over the wall and when the upstream depth is so great that the wall only produces a fall that is submerged downstream. In the range between these extremes the broad-crested weir can be used as an effective measuring device.

 

We can get a useful expression for the flow over the weir if we ignore friction over the crest of the weir and apply our usual physics of channel flow. This broad-crested weir is just another hump in the bed of a channel and steady flow over it will occur when the critical depth occurs somewhere on the crest. I have shown one free surface profile in figure 10-25. In this profile the surface falls to the critical depth somewhere just beyond the end of the radius and then remains steady until the fall at the down stream edge.

 

We must have a datum level for the specific energy and, as we saw for the hump used previously, the datum must be the same for the flow both upstream and over the crest. We cannot use the upstream depth because it might vary over time due to silting so we must use the crest of the weir.

For critical flow :-  where  is the critical depth for a flow per unit width of . From this we get .

 

We also have for critical flow  where  is the specific energy reckoned from the crest of the weir.

From these we get  where  is the width of the weir and  the volume flow and, as the kinetic energy in the upstream flow is small  can be put equal to the upstream depth relative to the crest say .

 

Then :-                   where  are in metres     

 

This is an interesting outcome because it gives an expression for flow over the wall that can be used with only one measurement, that is, the upstream depth above the crest. This expression can be exploited in the design of a practical device for measuring flow.

 

No doubt weirs of all sorts were in use long before this physics was first derived. They would have been calibrated, perhaps by measuring the velocity using double floats at some point upstream where the area could be measured. The evolution of the physics above gave a calibration expression that was probably just as accurate without direct calibration. That accuracy comes from the facts that the loss in converging flow is small and that, in practical weirs, the velocity distribution is not far from being uniform. However the expression is only applicable if the flow on the crest of the wall is critical at some point. This is a constraint that would not apply if the weir had been directly calibrated.

 

 The actual flow is affected by friction and the profile must be one where the depth falls below the critical and then rises to the critical depth at the fall at the discharge edge. The problem then becomes that of designing a weir profile that will have the critical depth somewhere on its crest for the range of flows that are expected. We have already noted the fact that the weir can be overwhelmed by an excessive depth downstream and the weir cannot then be used with this calibration expression to measure flow. At the other extreme, at very low flow the flow on the crest of the weir will be chaotic as a result of encrustation etc. and this invalidates the calibration expression.

 

One way of extending the measuring range of the weir is to let the crest slope away from the radius. Sloping the crest extends the range of low flows that can be measured by producing critical conditions near to the end of the radius and rapid flow over the crest. Figure 10-24 shows that, as the upstream depth increases, the point at which critical depth occurs advances towards the fall and that the approach to the fall extends towards the radius. Extending the length of the crest would clearly extend the range of high flows that can be measured. Unfortunately the extension of the length of the crest, when coupled with a slope, impairs the validity of the calibration expression for high flows and the greater the slope the worse the calibration expression becomes. As usual a compromise has to be made and the designer must determine the maximum depth over the weir for which the flow is critical. Computer methods may be used to put free surface profiles to different proposed weir profiles but the outcome has to be taken in the light of experience.

 

I think that one must be careful when assessing such a device as this broad-crested weir. We all tend to look for accuracy in measuring devices and deem those that are inherently inaccurate as not really satisfactory but just suppose that the depth on the crest of a weir had been measured daily on the same weir over say 100 years. It would not much matter whether the calibration expression was accurate because information can be extracted about long-term trends in the change of flow, and, depending on what information was sought, on other things as well. Furthermore, if the shape of the weir has been unchanged or if records existed of any changes in shape, it may be possible to improve the calibration expression in the light of changes in the analytical tools available to us now and in the future. A broad crested weir is much better than nothing.