Soil Sample
A test is conducted on a sample to determine a soil’s hydraulic conductivity. The sample is a 50 cm long cylindrical container with a cross sectional diameter of 10 cm. If the sample is subjected to a 75 cm head and a flow rate of 10 cm^3/min, what is the soil’s hydraulic conductivity?
Expand Hint
Darcy’s Law:
$$$Q=KA\frac{dh}{dx}$$$
where
$$Q$$
is the discharge rate,
$$K$$
is the hydraulic conductivity,
$$h$$
is the hydraulic head,
$$A$$
is the cross-sectional flow area, and
$$x$$
is the length.
Hint 2
You can keep the units in cm/min.
Darcy’s Law:
$$$Q=KA\frac{dh}{dx}$$$
where
$$Q$$
is the discharge rate,
$$K$$
is the hydraulic conductivity,
$$h$$
is the hydraulic head,
$$A$$
is the cross-sectional flow area, and
$$x$$
is the length.
Solving for hydraulic conductivity:
$$$K=\frac{Q\cdot dx}{A\cdot dh}=\frac{10cm^3/min(50cm)}{\pi (10cm/2)^2(75cm)}$$$
$$$=\frac{500cm^4/min}{\pi (25cm^2)(75cm)}=\frac{500cm/min}{5,887.5}=0.085\:cm/min$$$
0.085 cm/min
Time Analysis
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