Editor: In 1856 Henry Darcy described a series of experiments with flows of water through sand whereby he established the equation KH=Q; K times H equals Q; K is hydraulic conductivity, H is hydraulic gradient potential, Q is water flow current.

If we make K=1 then we have H=Q; a field of force equals a field of flow. And that’s what Darcy’s law is, a relationship between impressed force vector H and flow vector Q. A vector is a quantity which has a magnitude (a number), and a direction in space. Note: H and Q always point in the same direction.

Embedded in conductivity K are the properties of water and the sandstone matrix. K is a scalar quantity, just a number, with units such that force vector H is compatible with flow vector Q. Isaac Newton says: "An impressed Force is an Action exercised upon a Body, in order to change its state of Rest or uniform Motion in a straight Line."

Vector H is composed of two vectors: (1) gravity G pointing straight down, and (2) the pressure gradient vector P which points from higher pressure towards lower pressure. Not mentioned in P is a fluid density term, which makes the units of H, G, and P the same, force per unit, mass. Newton tells us how to combine G and P to get H: "If a Body be acted upon by two Forces, it will describe the Diagonal of a Parallelogram by both the Forces together, in the same Time that it will describe the Sides by those Forces separately."

Thus, for a native confined aquifer (CA), G points down, the sense of P will be towards the surface and H will point towards the surface and Q will have an upward sense, hence exfiltration.

When you pump water from a CA you lower the pressure, P eventually does not cancel G but adds to it and H and Q have a downward sense, hence infiltration. As long as the Winter River well fields pump water from the CA, problems will persist on the North Shore.

Tony Lloyd,

Mount Stewart