Physics for Geologists, Second edition

Fluids and fluid flow 125
Figure 12.7 Heads. The pressure head (plpg), elevation head (2, negative when
below the datum), and total head (h), which is the algebraic sum of
the other two.
constant. In fluid flow in rocks the velocity head is negligibly small and is
neglected. The total head is proportional to the energy of the water (lacking
only the factor g).
Real liquids are not ideal, and energy will be lost to heat, leading to a loss
of total head as the real liquid moves.
Fluid flow in rocks
Henry Darcy (note the spelling, Henry not Henri, no apostrophe in Darcy)
was an engineer responsible for water supply in the town of Dijon in France,
and he conducted experiments to determine the effect of sand filters on the
flow of water through pipes. He published the results in 1856.
Darcy filled a cylinder with sand, supported on a fine mesh, in apparatus
shown diagrammatically in Figure 12.8. Manometers were placed near the
top and bottom of the sand, and water was passed through the sand in the
cylinder. The volumetric rate of flow was measured, as were the elevations of
the water1 in the manometers (Figure 12.9). Darcy observed that 'for sands
of the same nature' the flow was proportional to the difference in elevation
of the levels in the manometers, and to the area normal to flow, and inversely
proportional to the length of the sand:
1 Darcy actually used mercury manometers, but it is simpler to treat them as water manometers
here.
Copyright 2002 by Richard E. Chapman