## 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?

##
__
__**Hint**

**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**

**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