Calculating Alluvial Aquifer Flow Rate
This problem requires calculating the flow rate ($q$) of groundwater in an alluvial aquifer using Darcy's Law.
Applying Darcy's Law
Darcy's Law states that the flow rate ($q$) per unit width of an aquifer is the product of its hydraulic conductivity ($K$) and the hydraulic gradient ($I$). The formula is:
$ q = K \times I $
Given:
- Hydraulic conductivity ($K$) = 105 m/day
- Hydraulic gradient ($I$) = 0.01
Substitute the given values into the formula:
$ q = 105 \text{ m/day} \times 0.01 $
Result Calculation
Performing the multiplication:
$ q = 1.05 \text{ m/day} $
The question asks to round the answer to 2 decimal places. The calculated value is already precise to 2 decimal places.
Verification
The calculated flow rate is 1.05 m/day. This value lies between 1 and 1.1, as stated in the provided answer criteria.
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]
- 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]
- The hydraulic conductivity (K) of an isotropic aquifer is 10 m/day. If the hydraulic head within the aquifer drops 4 m over a distance of 750 m, the groundwater flow velocity within the aquifer is _________ m/day.
(Up to third decimal place)
