Browsing IJAFR, volume 44, 2005 by Subject "Darcy's Law"
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The Flow of Water Through GravelsThe linear flow law of Darcy, relating the flux to the hydraulic gradient by a constant of proportionality, the hydraulic conductivity (K), is almost universally employed to analyse and predict the flow of fluids through soils and aquifers. Laminar flow is a prerequisite for its application and while not a problem in soils, it may be problematic in high velocity flows through gravel aquifers and drains. In the present study, the velocity of water flow through 30 screened gravel aggregates, comprising pit and broken stone gravels and ranging in particle diameter from 38.1 to 1.6 mm was measured. Some of the aggregates were reconstituted, derived by combining in various proportions fractions from laboratory screenings. The experimental arrangement comprised a 1.53-m long, 60-mm bore PVC smooth-walled pipe with retainer screens at both ends. This pipe was carefully packed with the particular gravel aggregate in 0.5 kg aliquots, placed horizontally on adjustable supports and connected to a 3-m3 reservoir held at a constant level. Hydraulic gradients applied were generally in the range 0.05–0.56. Each test was repeated at least twice. The flow of water through the gravels did not obey Darcy’s Law. The relationship between velocity, v (m/s), and the hydraulic gradient (i) was of the form, v = aib , with a and b (–) constants for a particular gravel. Darcy’s Law can be applied by considering a gradient-dependent hydraulic conductivity, v = K(i), from which K(i) = aib–1. Under unit gradient K(i) = a. In the coarser gravel aggregates, the value of b approached 0.5, similar to that for turbulent flow in roughwalled pipes. In fine-particle gravels, b tended toward unity indicating that Darcy’s Law could be applied without too much error. Results of tests in this series were in good agreement with those from another laboratory. Log-log curves and equations relating K(i) of individual aggregates to i are provided. K(i) values ranged over two orders of magnitude from 120,000 m/day for coarse gravel to about 700 m/day for a 4.76 to 1.6 mm gravel. There were very large declines in K(i) with increase in i in coarse gravels and small declines in the finer gravels. Results are discussed in relation to drainage and filter gravels and gravel aquifers.