Problem 55825. Measure the hydraulic conductivity with a constant-head permeameter
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 , or the difference in water levels between the standpipe and outlet, is constant.
The hydraulic conductivity can then be determined from Darcy’s law
where the head gradient is simply . Darcy’s law applies when a Reynolds number based on the specific discharge and representative diameter d of the soil grains is less than (approximately) 1—that is,
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:
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 and .
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