SUBSIDIOS Y SUBVENCIONES

of the stream (Fig. 6.23(a)). The bubbles rising to the surface with a constant terminal speed Vr are displaced downstream a distance L at the surface by the effects of the

velocity of the flow as the bubbles rise. In a unit width at a point across the channel, the discharge q over the total depth is given by:

where is the mean surface displacement of the bubbles at that point. The total discharge of the river is obtained from:

where n is the number of points across the river and ∆bi is the width of a segment.

From Fig. 6.23(b) it can therefore be seen that:

The area A is obtained in the field by taking photographs of the bubble pattern and then using a microcomputer technique to calculate area A from the photographic prints allowing for the orientation of the camera which is sited on one bank. From experiment it has been found that a mean value for Vr of 0.218 m s−1, for the particular nozzles used, in

depths up to 5 m gives an error of less than 2 %. When calibrated with the discharges over a weir, the integrating float technique gave a range of errors from −6 to +10 % in Q. Difficulties occur when the line of bubbles is indistinct in the turbulence of high flows. The effectiveness of the method diminishes with increase in river width, but for over 50 m the water surface can be photographed in sections. The method is a very economical alternative to standard gauging procedures. Its applicability has been tested in several flow conditions but in the future its main contribution is likely to be in the measurement

of controlled flows, e.g. in canals, since substantial difficulties have been encountered in its application in natural rivers.

References

Ackers, P., White, W.R., Perkins, J.A. and Harrison, A.J.M. (1978). Weirs and Flumes for Flow

Measurement. John Wiley. 327 pp.

Brater, E.F. and King, H.W. (1976). Handbook of Hydraulics, 6th ed. McGraw-Hill.

British Standards Institution (various dates). Methods of Measurement of Liquid Flow in Open

Channels. BS 3680.

Chow, Ven Te (1959). Open Channel Hydraulics. McGraw-Hill, 680 pp.

Francis, J.R.D. and Minton, P. (1984). Civil Engineering Hydraulies, 5th ed. Arnold, 400 pp. Grover, N.C. and Harrington, A.W. (1966). Stream Flow, Measurements, Records and Their Uses.

Dover Publications, 363 pp.

Herschy, R.W. (ed.) (1978). Hydrometry, Principles and Practices. John Wiley, 511 pp.

Herschy, R.W., White, W.R. and Whitehead, E. (1977). The Design of Crump Weirs. Tech. Memo. No. 8. DOE Water Data Unit.

Marsh, T.J. (1988). ‘The acquisition and archiving of river-flow data-past and present’, in

Hydrological Data: 1986. Institute of Hydrology.

Rantz, S.E. et al. (1982). US Geological Survey Water Supply. Paper 2175, Vol. I, 284 pp. Raudkivi, A.J. (1990). Loose Boundary Hydraulies. 3rd ed., Pergamon Press, 538 pp. Richards, K. (1982). Rivers; Form and Process in Alluvial Channels. Methuen, 358 pp.

Sargent, D.M. (1981). ‘The development of a viable method of streamflow measurement using the integrating float technique.’ Proc. Inst. Civ. Eng., 71(2), 1–15.

White, W.R., Bettess, R. and Paris, E. (1982). ‘Analytical approach to River Regimes’. ASCE, 108, HY10, 1179–1193.

7

Groundwater

In Chapter 5 on Soil Moisture, the introduction to the complexities of water storage below the ground surface confined attention to the water held in the soil matrix. Water was considered in the static state. In evaluating ground-water on a larger scale, it is necessary to deal with groundwater in motion. The degree of difficulty that arises in calculating groundwater movement is affected by whether the ground is saturated or not, since in the aeration zone the two-phase mixture of vapour and liquid in the pores or voids causes hysteresis in the pressure water content to permeability relationships. When the voids are filled completely with water, those complex relationships are no longer relevant and the more familiar concepts of single-phase liquid flow can be applied, but generally not without some simplifying assumptions.

Before proceeding to describe groundwater flow, it is pertinent to consider the sources of groundwater. Most of the water stored in the ground comes from residual precipitation at the surface infiltrating into the top soil and percolating downwards through the porous layers. Certain quantities pass into the ground along river banks at times of high flows and these generally sustain the flow by returning water to the rivers as the flow recedes. However, the longer term renewal of groundwater is brought about by infiltration of rainfall over a catchment area.

7.1 Infiltration

When a soil is below field capacity and surplus rainfall collects on the surface, the water crosses the interface into the ground at an initial rate (f0) dependent on the existing soil

moisture content. As the rainfall supply continues, the rate of infiltration decreases as the soil becomes wetter and less able to take up water. The typical curve of infiltration rate with time shown in Fig. 7.1 reduces to a constant value fc, the infiltration capacity, which

is mainly dependent on soil type. From Chapter 5, it will be appreciated that sandy soils have higher infiltration capacities than fine clay soils.

The rate at which water infiltrates into the soil can be measured by an infiltrometer. The simplest method adds water to the ground surface contained within a 200 mm diameter tube set vertically into the soil. The water is supplied from a graduated burette and the water depth is restored to a constant level by measured additions at regular time intervals. The rate of infiltration is then easily calculated. To prevent horizontal dispersion below the tube the infiltrometer may consist of two concentric rings. The area within each ring is flooded as before, but it is the inner ring that gives the infiltration measurement with the water draining in the outer ring prevent-ing lateral seepage from the central core. Another method of assessing infiltration uses a watertight sample plot of ground on to which simulated rainfall of known uniform intensity is sprayed from special

nozzles. The surface runoff from the plot is measured, and by sequential operations of the ‘infiltrometer’, assessments of the volume of water retained in the surface depressions and detained in the soil can be made. An infiltration rate curve can again be estimated up to the point when, with the soil at field capacity, the constant infiltration capacity is obtained. Full details are given by Musgrave and Holtan (1964). From either method, infiltration curves can be compiled for a range of soil types and for different vegetational covers.

When the hydrologist is required to model the infiltration process, two formulae are often used:

(a) Horton (1940) suggested that the form of the curve given in Fig. 7.1 is exponential and that this might be expected from infiltration being a decay process as the soil voids become exhausted. He proposed that the infiltration rate at any time t from the start of an adequate supply of rainfall is:

f

=f

+(f

−f

)exp(−kt)

_(7.1)

The values of fc and of k, the exponential decay constant, are dependent on soil

type and vegetation.

(b) Philip has studied infiltration and soil water movement extensively for many years. (Philip, (1960) gives a review.) He developed a simple formula for infiltration rate related to time:

(7.2)