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Darcy's law; tests for permeability

Short answer

Darcy's law states discharge velocity v = k i with Q = k i A, where i = h/L, valid for laminar flow. Laboratory tests: constant head (coarse soils), falling head (fine soils), indirect methods (consolidation, Hazen). Field tests: pumping out, pumping in, packer, and tracer tests.

Explain Darcy's law in regard to discharge velocity. Write down the names of different tests done to find the coefficient of permeability of the soil, both in the laboratory and field.

Darcy's law states that for laminar flow through a saturated soil, the discharge velocity is directly proportional to the hydraulic gradient:

v=k i,Q=k i Av = k\,i, \qquad Q = k\,i\,A

where v=Q/Av = Q/A is the discharge velocity (the flow per unit gross area, not the actual velocity in the pores), i=h/Li = h/L is the hydraulic gradient and kk is the coefficient of permeability. The law is valid for a Reynolds number below about 1 (fine sands, silts and clays); it fails in coarse gravel (turbulent flow).

Tests to find k

Laboratory

  • Constant head permeability test (for coarse-grained soils)
  • Falling (variable) head permeability test (for fine-grained soils)
  • Indirect: from consolidation test data, horizontal capillarity test, empirical formulae (Hazen's, k=CD102k = C D_{10}^2)

Field

  • Pumping out test (from wells)
  • Pumping in test
  • Borehole (auger hole) tests
  • Packer test (for rock)
  • Tracer tests

✓ Answer checked by Claude Opus 5.5 (high effort)

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