This solution explains how to calculate the Darcy flux (specific discharge) in a confined aquifer using the provided information and Darcy's Law.
Aquifer Darcy Flux Calculation
Given Data
- Coefficient of Permeability ($K$): 40 m/day
- Horizontal distance between wells ($L$): 800 m
- Water surface elevation difference ($\Delta h$): 50 m - 45 m = 5 m
Darcy's Law Formula
Darcy's Law relates specific discharge ($q$) to the coefficient of permeability ($K$) and the hydraulic gradient ($i$):
$ q = K \cdot i $
The hydraulic gradient ($i$) is defined as the change in hydraulic head ($\Delta h$) over the length of flow ($L$):
$ i = \frac{\Delta h}{L} $
Calculation Steps
- Calculate the Hydraulic Gradient ($i$):
Substitute the given values for head difference and distance:
$ i = \frac{5 \text{ m}}{800 \text{ m}} = 0.00625 $
- Calculate the Darcy Flux ($q$):
Use Darcy's Law, substituting the calculated gradient and the given permeability:
$ q = (40 \text{ m/day}) \times (0.00625) $
$ q = 0.25 \text{ m/day} $
Result
The absolute value of Darcy flux through the aquifer is 0.25 m/day.
Important Questions from Hydrogeology (Darcy Flow/Flow Rate)
- A soil mass comprises two horizontal layers (of equal thickness and equal width) stacked one above the other. The hydraulic conductivities of the two layers are $5 \times 10^{-2}$ cm/s and $3 \times 10^{-2}$ cm/s. Considering Darcian flow of water and same hydraulic gradient for both the layers, the effective hydraulic conductivity of the soil mass in cm/s is ________ (rounded off to two decimal places).
- A cylindrical soil sample of 10 cm diameter is tested in a constant-head permeameter. A volume of 250 cm$^3$ of water is collected in 5 minutes when the constant-head difference between tapping points 15 cm apart is 5 cm. Considering Darcy flow, the absolute value of coefficient of permeability in cm/s is _________ ($\pi = 3.14$) [round off to 3 decimal places]
- For a productive alluvial aquifer with hydraulic conductivity = 105 m/day and hydraulic gradient = 0.01, the flow rate is _______ m/day. [round off to 2 decimal places]
- The cross section of a river channel is approximated by a trapezium. The river has an average channel width of 40 m and average depth of 3 m. If the average flow speed is 2 m/s, the discharge rate is __________ m³/s. [in integer]
- A constant-head permeability test was performed on a vertical sand column of height 40 cm and cross-sectional area of 25 cm². During the test, when the loss of head was 50 cm, the volume of water collected in 2 minutes was 300 cm³. Applying Darcy's law, the calculated coefficient of permeability of the sand column is __________ cm/sec. [round off to 2 decimal places]
