Calculating Water Table Drop in Unconfined Aquifer
The problem asks for the average drop in the water table ($\Delta h$) in an unconfined aquifer due to pumping. We are given the watershed area ($A$), the volume of water pumped ($V$), and the specific yield ($S_y$).
Given Data:
- Watershed Area, $A = 100$ $km^2$
- Volume Pumped, $V = 30$ million $m^3 = 30 \times 10^6$ $m^3$
- Specific Yield, $S_y = 0.20$
- Hydraulic conductivity, $K = 15$ m $day^{-1}$ (Note: $K$ is not required for this specific calculation)
Required Calculation:
The relationship between the volume of water pumped from an unconfined aquifer and the resulting drop in water table is given by the equation:
$ V = A \times S_y \times \Delta h $We need to rearrange this formula to solve for the water table drop, $\Delta h$.
Step-by-Step Solution:
- Convert Area Units: Convert the watershed area from $km^2$ to $m^2$. $ A = 100 \text{ } km^2 = 100 \times (1000 \text{ m})^2 = 100 \times 10^6 \text{ } m^2 = 1 \times 10^8 \text{ } m^2 $
- Rearrange Formula: Solve the storage equation for $\Delta h$. $ \Delta h = \frac{V}{A \times S_y} $
- Substitute Values: Plug the given and converted values into the formula. $ \Delta h = \frac{30 \times 10^6 \text{ } m^3}{(1 \times 10^8 \text{ } m^2) \times 0.20} $
- Calculate Result: Perform the calculation. $ \Delta h = \frac{30 \times 10^6}{0.20 \times 10^8} = \frac{30 \times 10^6}{20 \times 10^6} = \frac{30}{20} $ $ \Delta h = 1.5 \text{ meters} $
Conclusion:
The average drop of the water table over the watershed is 1.5 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.
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_______
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
