Two reservoirs having a difference of 20 m in their water surface elevations are connected through a confined aquifer (thickness = 5 m, length = 2 km, hydraulic conductivity $K = 3 \times 10^{-3}$ m/s, and porosity $\eta = 0.3$) as shown in the following figure (drawn not to scale). 
If the Reservoir 1 is contaminated by a pollutant then the time (in days, rounded off to one decimal place) taken by the pollutant to reach to the Reservoir 2 under advection will be ________
Two reservoirs having a difference of 20 m in their water surface elevations are connected through a confined aquifer. A pollutant enters Reservoir 1 and travels toward Reservoir 2 by advection. The time required for the pollutant to reach Reservoir 2 is to be determined.
Given Data
- Difference in water levels: \( \Delta h = 20 \, \text{m} \)
- Length of aquifer: \( L = 2 \, \text{km} = 2000 \, \text{m} \)
- Thickness of aquifer: \( 5 \, \text{m} \)
- Hydraulic conductivity: \( K = 3 \times 10^{-3} \, \text{m/s} \)
- Porosity: \( \eta = 0.3 \)
Step 1: Hydraulic Gradient
The hydraulic gradient is given by:
$$ i = \frac{\Delta h}{L} $$
Substituting values:
$$ i = \frac{20}{2000} = 0.01 $$
Step 2: Darcy (Discharge) Velocity
Using Darcy’s law:
$$ q = K i $$
Substitute values:
$$ q = (3 \times 10^{-3})(0.01) = 3 \times 10^{-5} \, \text{m/s} $$
This is the Darcy velocity, not the actual velocity of groundwater particles.
Step 3: Seepage (Average Linear) Velocity
The actual velocity at which the pollutant moves (seepage velocity) is:
$$ v = \frac{q}{\eta} $$
Substituting:
$$ v = \frac{3 \times 10^{-5}}{0.3} = 1 \times 10^{-4} \, \text{m/s} $$
Step 4: Time of Travel
Travel time is:
$$ t = \frac{L}{v} $$
Substitute values:
$$ t = \frac{2000}{1 \times 10^{-4}} = 2 \times 10^{7} \, \text{s} $$
Step 5: Convert Time to Days
$$ 1 \text{ day} = 86{,}400 \text{ s} $$
$$ t = \frac{2 \times 10^{7}}{86{,}400} \approx 231.5 \text{ days} $$
Important Questions from Darcy Law
- A homogeneous isotropic confined aquifer of uniform thickness $30 \text{ m}$ has hydraulic conductivity of $5 \text{ m/day}$ and porosity of $0.3$. There are two observation wells X and Y along a radial line from a fully penetrating pumping well at $100 \text{ m}$ and $200 \text{ m}$ distance, respectively. The well is pumped at a uniform rate to produce steady drawdown of $5 \text{ m}$ at X and $3 \text{ m}$ at Y. If a non-reactive pollutant enters at the observation well Y, then the time taken by the pollutant (under advection) to reach the observation well X is ________ days. (rounded off to two decimal places)
- The kinematic viscosity of glycerin and kerosene are 1.2 times and 0.95 times of that of water, respectively. Glycerin and kerosene flow through two identical porous media having same hydraulic gradient. Assuming Darcy's law is valid for the porous media, the ratio of flow rate of kerosene to that of glycerin is
Two fully penetrating wells are dug 1.4 km apart in a homogenous confined aquifer. The difference in their piezometric levels is 4.0 m. The groundwater flow is steady and unidirectional. If the aquifer has a hydraulic conductivity of $3.5\ m\cdot day^{-1}$ and effective porosity of 40%, the time taken for water to move from one well to the other in days is _____________. [in integer]
- In a field test of a geological formation of permeable soil (porosity = 20%), the hydraulic gradient was found to be 2%. The actual seepage velocity of the flow was found to be 0.0025 m/s. Assume that the flow is in the laminar regime. The permeability (K) of the aquifer is ________ m/s (rounded off to three decimal places).
