As in the measurement of precipitation, measurement of river discharge is a sampling procedure. For springs and very small streams, accurate volumetric quantities over timed intervals can be measured, and is called volumetric gauging. For a large stream, a continuous measure of one variable, river level (Section 7.3), is related to the spot measurements of discharge collected by dilution gauging methods (Section 7.5) or calculated from sampled values of the variables, velocity and area (so-called velocity-area methods; Section 7.4). Where velocity-area methods are used, the discharge of a river, Q, is normally obtained from the summation of the product of mean velocities in the vertical, v, and area of related segments, a, of the total cross-sectional area, A (Fig. 7.4; see Section 7.4.3). Thus,
The fixed cross-sectional area is determined with relative ease, but it is much more difficult to ensure consistent measurements of the flow velocities to obtain values of v.
A single estimate of river discharge can be made readily on occasions when access to the whole width of the river is feasible and the necessary velocities and depths can be measured. However, such 'one-off' values are of limited use to the hydrologist. Continuous monitoring of the river flow is essential for assessing water availability. The continuous recording of velocities across a river is normally not a practical proposition for large rivers, ultrasonic (doppler) flow meters are sometimes used to measure a continuous record of velocity in small streams. It is, however, relatively simple to arrange for the continuous measurement of the river level. A fixed and constant relationship is required between the river level (called stage) and the discharge at the gauging site. This occurs along stretches of a regular channel where the flow is slow and uniform and the stage-discharge relationship is under 'channel control'. In reaches where the flow is usually non-uniform, it is important to arrange a unique relationship between water level and discharge. It is therefore necessary either to find a natural 'bed control' as in Fig. 7.3, where critical flow occurs over some rapids with a tranquil pool upstream, or to build a control structure across the bed of the river making the flow pass through critical conditions (Fig. 7.4b). Where a control structure has been built, discharge is sometimes described as being measured by structural methods (Section 7.6). In both cases, the discharge, Q, is a unique function of yc and hence of the water level just upstream of the control. In establishing a permanent critical section gauging station, care has to be taken to verify that the bed or structural control regulates the upstream flow for all discharges. At very high flows, the section of critical flow may be 'drowned
P = Wetted perimeter A = Total cross-sectional area Hydraulic mean depth R = A/P b x y = a, area of segment
Fig. 7.4 Channel definitions, where (a) is the cross-section, and (b) is the profile for y ^ yc and H is head.
out' as higher levels downstream of the control eliminate the critical depth. Then the flow depths will be greater than yc throughout the control and the relationship between the upstream water level and discharge reverts to 'channel control'.
At a gauging site, when the flow is contained within the known cross-section and is controlled by a bed structure, then the discharge Q is a function of H (head), the difference in height between the water level upstream and the crest level of the bed control (Fig. 7.4b). The functional stage-discharge relationship or rating curve (see Section 7.7) is established by either measuring discharge directly (dilution methods) or by estimating Q from sampled measurements of either velocity across the channel (velocity-area methods), when it is convenient, for different values of H. Regularly observed or continuously recorded stages or river levels can then be converted to corresponding discharge time series. For a structural control, e.g. a weir built to standard specifications, the stage-discharge or Q^H relationship is known, and velocity-area or dilution measurements are used only as a check on the weir construction and calibration.
After flood flows, cross-sectional dimensions at a gauging station should be checked for erosion-deposition-related changes and, if necessary, the river level-discharge relationships amended by a further series of velocity-area measurements.
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