Flumes are particularly suitable for small streams carrying a considerable fine sediment load. The upstream sub-critical flow is constricted by narrowing the channel, thereby causing increased velocity and a decrease in the depth. With a sufficient contraction of the channel width, the flow becomes critical in the throat of the flume and a standing wave is formed further downstream. The water level upstream of the flume can then be related directly to the discharge. A typical design is shown in Fig. 7.20. Such critical depth flumes can have a variety of cross-sectional shapes.
The illustration shows a plain rectangular section with a horizontal invert (bed profile), but trapezoidal sections are used to contain a wider range of discharges and U-shaped sections are favoured in urban areas for more confined flows and sewage effluents. Where there are only small quantities of sediment, the length of the flume can be shortened by introducing a hump in the invert to reduce the depth of flow and thus
induce critical flow more quickly in the contraction, but the flume must be inspected regularly and any sediment deposits cleared. Relating the discharge for a rectangular cross-section to the measured head, H, the general form of the equation is:
where b is the throat width and K is a coefficient based on analysis and experiment. For the derivation of K, the reader is referred to BS ISO 4359 (1983). With flumes built to that standard, Q may be assessed to within 2 per cent without the need for any field calibration. There are many different flume designs that have been built to serve various purposes in measuring a range of flow conditions. These are described fully in Herschy (2009).
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