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Unformatted text preview: linearly from
zero at the axis to w at the wall. It is claimed that this is
also true, at least in the time mean, for fully developed turbulent flow. Can you verify this claim analytically?
W6.4 A porous medium consists of many tiny tortuous passages,
and Reynolds numbers based on pore size are usually very
low, of order unity. In 1856 H. Darcy proposed that the pressure gradient in a porous medium was directly proportional
to the volume-averaged velocity V of the fluid: V
where K is termed the permeability of the medium. This is
now called Darcy’s law of porous flow. Can you make a
Poiseuille flow model of porous-media flow which verifies
Darcy’s law? Meanwhile, as the Reynolds number increases,
so that VK1/2/
1, the pressure drop becomes nonlinear,
as was shown experimentally by P. H. Forscheimer as early
as 1782. The flow is still decidedly laminar, yet the pressure gradient is quadratic:
p v v | | e-Text Main Menu | V CVV Darcy-Forscheimer law where C is an empirical constant. Can you explain the reason for this nonlinear...
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- Spring '08