Question:hard

An aquifer has a surface area of 100 km2. With no recharge, assume that pumping out \(2 \times 10^{7}\) m3 of ground water resulted in a drop of the water table by 6 m. If the aquifer has a specific retention of 15%, then the porosity of the aquifer is % (rounded off to one decimal place).

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Specific yield = pumped volume / (area x drop). Porosity = specific yield + specific retention.
Updated On: Aug 14, 2026
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Correct Answer: 18.3

Solution and Explanation

Step 1: Think about the water column drained.
As the water table drops by 6 m over 100 km$^2$, the aquifer effectively drains a slab of rock 6 m thick across that whole area. The volume of that slab is
\[ V_{slab}=A\times\Delta h \]

Step 2: Work out the slab volume.
$1$ km$^2$ is $10^6$ m$^2$, so $A=100\times10^6=10^8$ m$^2$. With $\Delta h=6$ m,
\[ V_{slab}=10^8\times6=6\times10^8\ \text{m}^3 \]

Step 3: Compare pumped water to the slab volume.
Only part of that slab's pore space actually gave up water; the rest is specific retention. The fraction that gave up water is the specific yield, found by dividing the actual water pumped by the slab volume:
\[ S_y=\frac{V_{pumped}}{V_{slab}}=\frac{2\times10^{7}}{6\times10^{8}} \]
\[ S_y=0.0333=3.33\% \]

Step 4: Add back the water that stayed behind.
Total porosity is the sum of what drained out and what clung to the grains, that is specific yield plus specific retention:
\[ n=S_y+S_r=3.33\%+15\%=18.33\% \]

Step 5: Round to the asked precision.
The question wants the answer to one decimal place.
\[ \boxed{18.3\%} \]
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