Darcy
A test is conducted on a sample to determine a soil’s flow rate. The sample is a 40 cm long cylindrical container with a cross sectional diameter of 5 cm and a measured hydraulic conductivity of 0.1 cm/min. If the sample is subjected to a 80 cm head, what is the soil’s discharge rate?
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.
$$$Q=\frac{(0.1cm/min)(\pi/4)(5cm)^2(80cm)}{40cm}$$$
$$$=\frac{(0.1cm)(\pi)(25cm^2)(2)}{4min}=3.93\:\frac{cm^3}{min}$$$
$$$3.93\:\frac{cm^3}{min}$$$
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
Similar Problems from FE Sub Section: Darcy's Law
320. Soil Sample
Similar Problems from FE Section: Hydrology/Water Resources
079. Flow Rate
320. Soil Sample
368. Elevated Storage Tank