River Channel Area Calculation
The cross-sectional area ($A$) of the river channel is needed to calculate the discharge rate. Given the average channel width ($W$) and average depth ($D$), the area can be calculated as:
$ A = W \times D $
Substitute the given values:
- Width ($W$) = 40 m
- Depth ($D$) = 3 m
$ A = 40 \, \text{m} \times 3 \, \text{m} $
$ A = 120 \, \text{m}^2 $
Discharge Rate Calculation
The discharge rate ($Q$) is the volume of water flowing per unit time. It is calculated using the formula:
$ Q = A \times V $
Where $A$ is the cross-sectional area and $V$ is the average flow speed.
- Area ($A$) = 120 m²
- Flow speed ($V$) = 2 m/s
Substitute these values into the discharge formula:
$ Q = 120 \, \text{m}^2 \times 2 \, \text{m/s} $
$ Q = 240 \, \text{m}^3/\text{s} $
The discharge rate is 240 m³/s. Since the question asks for an integer value, the answer is 240.
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]
- 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)
