Weirs constitute a more versatile group of structures providing restriction to the depth rather than the width of the flow in a river or stream channel. A distinct sharp break in the bed profile is constructed and this creates a raised upstream sub-critical flow, a critical flow over the weir and super-critical flow downstream. The wide variety of weir types can provide for the measurement of discharges ranging from a few litres per second to many hundreds of cubic metres per second. In each type, the upstream head is again uniquely related to the discharge over the crest of the structure where the flow passes through critical conditions.

For gauging clear water in small streams or narrow man-made channels, sharp-crested or thin-plate weirs are used. These give highly accurate discharge measurements but to ensure the accuracy of the stage-discharge relationship, there must be atmospheric pressure underneath the nappe of the flow over the weir (Fig. 7.21). Thin plate weirs can be full-width weirs extending across the total width of a rectangular approach channel (Fig. 7.21a) or contracted weirs as in Fig. 7.21b and c. The shape of the weir may be rectangular or trapezoidal or have a triangular cross-section, a V-notch. The angle of the V-notch, 9, may have various values, the most common being 90° and 45°, though narrower angles are used for drainage discharge recorders and 120° angle weirs are more common on flashy tropical streams.

The basic discharge equation for a rectangular sharp crested weir again takes the form,

but in finding K, allowances must be made to account for the channel geometry and the nature of the contraction. Such hydraulic details may be obtained from Ackers et al. (1978). For the V-notch weirs, the discharge formula becomes,

Tables of coefficients for thin-plate weirs are normally to be found in the specialist references (e.g. BS ISO 1438, 2008; Herschy, 2009).

(a) Outlet
Fig. 7.21 Thin plate weirs. (Reproduced (a) from P. Ackers, et al. (1978) Weirs and Flumes for Flow Measurement, by permission of John Wiley & Sons, Inc.; (b) and (c) from BS ISO 1438: 2008, by permission of BSI.)

For larger channels and natural rivers, there are several designs recommended for gauging stations and these are usually constructed in concrete. One of the simplest to build is the broad-crested (square-edged) or the rectangular-profile weir (Fig. 7.22). The discharge in terms of gauged head H is given by,

The length L of the weir, related to H and to P, the weir height, is very important since critical flow should be well established over the weir. However, separation of flow may occur at the upstream edge, and with increase in H, the pattern of flow and the coefficient, K, change. Considerable research has been done on the calibration of these weirs. The broad-crested weir with a curved upstream edge, also called the round-nosed horizontal-crested weir, gives an improved flow pattern over the weir with no flow separation at the upstream edge, and it is also less vulnerable to damage. The discharge formula is similarly dependent on the establishment of weir coefficients.

A special form of weir with a triangular profile was designed by E. S. Crump in 1952 (BS ISO 4360:2008). This ensured that the pattern of flow remained similar throughout the range of discharges and thus weir coefficients remained constant. In addition, by making additional head measurements just below the crest, as well as upstream, the Crump weir allows flow measurements to be estimated above the modular limit when the weir has drowned out at high flows. The geometry of the Crump weir is shown in Fig. 7.22a. The upstream slope of 1:2 and downstream slope of 1:5 produce

Fig. 7.22 Rectangular profile weir. (Reproduced from BS ISO 4360:2008, by permission of BSI.)

a well-controlled hydraulic jump on the downstream slope in the modular range. Improvement in the accuracy of very low flow measurement has been brought about by the compounding of the Crump weir across the width of the channel. Two or more separate crest sections at different levels may be built with sub-dividing piers to separate the flow. Such structures are designed individually to match the channel and flow conditions. A great deal of research effort has been put into the development of the Crump weir and many have been built in the UK.

The flat-V weir (Fig. 7.23b) is developed from an improvement on the Crump weir (BS ISO 4377, 2002: Fig. 7.23a). By making the shape of the crest across the channel into a shallow V-shape, low flows are measured more accurately in the confined central portion without the need for compounding. The triangular profile may be the same as the Crump weir, 1:2 upstream face and 1:5 downstream, but a profile with both slopes 1:2 is also used. This weir can also operate in the high non-modular flow range and several crest cross-sectional slopes have been calibrated. An extra advantage of the flat V-weir is that it passes sediment more readily than the Crump. Flat V-weirs, including those needing velocity-area measurements at higher stages, are also popular in the UK.

All these structures have a clear upper limit in their ability to measure the stream flow. Usually as the flow rate increases, downstream channel control causes such an increased downstream water level that a flume or weir is drowned out; the unique relationship hitherto existing between the stage or upstream level and the discharge in the so-called 'modular' range is thereafter lost. It is not always practicable to set crest levels in flumes and weirs sufficiently high to avoid the drowning out process at high flows since upstream riparian interests would object to raised water levels and out-of-bank flows at discharges previously within banks. In some cases where non-modular flow occurs regularly, discharges can be calculated by installing level gauges both upstream and downstream of the structure and using the conservation of momentum equation to calculate flow velocity (Ackers et al., 1978).

These structures are generally used for measuring low and medium flows; flood flows are not usually measurable with flumes and weirs. However, in a world-wide context, they are well suited to the smaller rivers of the UK. However, the potential effects of weir construction on fish migration can restrict the establishment of new structures, and the high cost of maintenance can lead to the closure of some stations where data are under-utilised. Furthermore, such structures are considered impracticable and/or prohibitively costly for single-purpose river gauging in rivers of continental proportions.

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