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GATE 2024 ES – Question 40

Water Resources and Environmental Hydraulics · Groundwater Resources · 2 marks · Multiple choice

Two isotropic homogeneous aquifer layers have thicknesses $h_1\ne h_2$ and horizontal conductivities $K_1,K_2$. Flow is parallel to stratification as shown. Find equivalent horizontal conductivity.

Diagram for GATE 2024 ES question 40
  1. $(K_1h_1+K_2h_2)/(h_1+h_2)$
  2. $(K_1+K_2)/2$
  3. $(K_1h_2+K_2h_1)/(h_1+h_2)$
  4. $\sqrt{K_1K_2}$

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Correct answer: (A) $(K_1h_1+K_2h_2)/(h_1+h_2)$

Explanation

Both layers experience the same hydraulic gradient i. Per unit width, total discharge is $q=i(K_1h_1+K_2h_2)$. The equivalent layer has thickness $h_1+h_2$ and discharge $iK_x(h_1+h_2)$. Equating gives the thickness-weighted arithmetic mean in **A**.

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