A constant-head permeameter is a device for measuring the hydraulic conductivity K of a soil sample. In this problem the sample is placed in a cylinder of length L and cross-sectional area A. By supplying a flow Q to a standpipe, water is maintained at a constant level so that the head difference Deltah, or the difference in water levels between the standpipe and outlet, is constant.
The hydraulic conductivity can then be determined from Darcy’s law
Q = -K(dh/dx)A
where the head gradient dh/dx is simply Deltah/L. Darcy’s law applies when a Reynolds number based on the specific discharge v = Q/A and representative diameter d of the soil grains is less than (approximately) 1—that is,
Re = vd/nu < 1
where ν is the kinematic viscosity of the fluid.
The Kozeny-Carman equation provides one way to relate the hydraulic conductivity to the representative grain diameter:
K = (gd^2/(180nu))(n^3/(1-n)^2)
where g is the acceleration of gravity and n is the porosity of the soil
Write a function that takes as input the flowrate, the head difference, porosity, and length and diameter of the cylinder holding the soil sample and returns the hydraulic conductivity and a flag indicating whether Darcy’s law is valid. Compute the conductivity using Darcy’s law regardless of its validity, and use g = 9.81 m/s^2 and nu = 10^{-6} m^2/s.
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