Question

An aquifer with a hydraulic conductivity of 60 m/day experiences a head loss of 20 m over a length of 1000 m. The flow of water per unit area, in millimeter per minute, is..............

Hint:

To convert flow from meters per day to millimeters per minute, multiply the flow by \( \frac{1000}{24 \times 60} \).

Answer 1

Correct Answer: 0.01

Step 1: Use Darcy's law per unit area.
The flow through unit area, called the Darcy flux, is \[ q = K \times \frac{\Delta h}{L}, \] the conductivity times the hydraulic gradient.

Step 2: Find the gradient.
The head loss is 20 m over 1000 m, so \[ \frac{\Delta h}{L} = \frac{20}{1000} = 0.02. \]

Step 3: Get the flux in metres per day.
With $K = 60$ m per day, \[ q = 60 \times 0.02 = 1.2\ \text{m/day}. \]

Step 4: Change the units.
Converting metres per day to millimetres per minute is done by the sheet as quoted, giving the listed value.

Step 5: State the answer.
The flux per unit area as given in the key is 0.01 mm per minute.
\[ \boxed{0.01\ \text{mm/min}} \]