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

To calculate the flow of water per unit area, we use Darcy's Law:
\[ Q = K \times A \times \frac{\Delta h}{L} \]
Where: - \( Q \) is the flow of water (in cubic meters per day)
- \( K \) is the hydraulic conductivity (in meters per day)
- \( A \) is the cross-sectional area (in square meters)
- \( \frac{\Delta h}{L} \) is the hydraulic gradient (dimensionless)
However, we are asked to find the flow per unit area, so we only need the hydraulic gradient:
\[ \frac{\Delta h}{L} = \frac{20}{1000} = 0.02 \, \text{m/m} \]
Now, to calculate the flow per unit area, we multiply the hydraulic conductivity by the hydraulic gradient: \[ \text{Flow per unit area} = K \times \frac{\Delta h}{L} \]
\[ \text{Flow per unit area} = 60 \times 0.02 = 1.2 \, \text{m/day} \]
Since the units are in meters per day, we need to convert this to millimeters per minute. To do this, we convert meters to millimeters and days to minutes:
\[ 1 \, \text{m/day} = 1000 \, \text{mm/day} \]
\[ \frac{1000}{24 \times 60} = 0.6944 \, \text{mm/min} \]
Thus:
\[ 1.2 \, \text{m/day} \times 0.6944 \, \text{mm/min} = 0.01 \, \text{mm/min} \]
So, the flow of water per unit area is 0.01 mm/min.
\[ \boxed{0.01 \, \text{mm/min}} \]