An unconfined aquifer extends over an area of $1 \text{ km}^2$ and has hydraulic conductivity, total porosity and specific retention of $20 \text{ m per day}, 30\%$ and $10\%$, respectively. After pumping some groundwater from this aquifer, the water table dropped to a depth of $20 \text{ m}$ from the ground level. If the water table was initially at $14.5 \text{ m}$ below the ground level, the change in groundwater storage in million cubic meters would be_______
Unconfined Aquifer Storage Change
To find the change in groundwater storage, we need to consider the volume of water released from the aquifer as the water table drops. This volume is related to the aquifer's area, the amount the water table drops (drawdown), and the aquifer's specific yield.
Calculating Specific Yield
For an unconfined aquifer, the specific yield ($S_y$) represents the volume of water drained per unit area per unit decline in the water table. It is calculated as the difference between total porosity ($n$) and specific retention ($S_r$).
- Total porosity ($n$): $30\% = 0.30$
- Specific retention ($S_r$): $10\% = 0.10$
- Specific Yield ($S_y$) = $n - S_r$
Calculation:
$ S_y = 0.30 - 0.10 = 0.20 $
Calculating Water Table Drop
The water table drop, or drawdown ($\Delta h$), is the difference between the initial and final water table levels.
- Initial water table depth: $14.5 \text{ m}$
- Final water table depth: $20 \text{ m}$
Calculation:
$ \Delta h = 20 \text{ m} - 14.5 \text{ m} = 5.5 \text{ m} $
Calculating Change in Groundwater Storage
The change in groundwater storage ($\Delta S$) is the product of the aquifer's area ($A$), the water table drop ($\Delta h$), and the specific yield ($S_y$).
- Area ($A$): $1 \text{ km}^2 = (1000 \text{ m})^2 = 1,000,000 \text{ m}^2$
- Water table drop ($\Delta h$): $5.5 \text{ m}$
- Specific Yield ($S_y$): $0.20$
Calculation:
$ \Delta S = A \times \Delta h \times S_y $
$ \Delta S = (1,000,000 \text{ m}^2) \times (5.5 \text{ m}) \times (0.20) $
$ \Delta S = 1,000,000 \times 1.1 \text{ m}^3 $
$ \Delta S = 1,100,000 \text{ m}^3 $
The change in groundwater storage is $1,100,000$ cubic meters.
Important Questions from Groundwater Occurrence
An unconfined aquifer of areal extent $20 \text{ km} \times 20 \text{ km}$ has hydraulic conductivity of $4 \text{ m/day}$, porosity of $0.32$, and storage coefficient (specific yield) of $0.18$. If the initial saturated thickness of the aquifer is $30 \text{ m}$, and $4\times10^8 \text{ m}^3$ of water is extracted from the aquifer, then the decline in the saturated thickness is _____________ (rounded off to two decimal places) m.
Match the following items between Column I and Column II with the most appropriate combinations:
Column I Column II P Properties of confined and semi- confined aquifers 1 Perched aquifer Q Property of an unconfined aquifer 2 Coefficient of storage R Property of semi-confined aquifer 3 Specific yield S A special case of an unconfined aquifer 4 Leakage factor A fully penetrating well is installed in a homogenous and isotropic confined aquifer. The aquifer has uniform thickness of 16 m and hydraulic conductivity of 25 m/d. Water is being pumped out from the well at a constant rate of $0.1 \text{ } m^3/s$ till steady state condition is reached. If a drawdown of 3.5 m is observed at a distance of 75 m from the well then the drawdown at a distance of 150 m from the well will be________ (in m, rounded off to two decimal places).
- One of the key assumptions made by Dupuit-Forchheimer about the flow behavior in the porous medium towards subsurface drains is
An underground hazardous waste storage tank is leaking. The contaminant concentration directly beneath the site is 0.5 mg/L. The contaminant is travelling at an effective rate of 0.4 m per day towards a water well which is 2 km away.
Assume that the degradation of the contaminant follows a first order reaction, and the initial concentration of the contaminant becomes half in 10 years.
In this case, the contaminant concentration expected at the well under steady state conditions is ________ mg/L (rounded off to two decimal places).
