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GATE 2023 AG – Question 58

Soil and Water Conservation Engineering · Soil Mechanics · 2 marks · Numerical answer

An anisotropic earth dam is 52 m high with 2 m freeboard. Horizontal/vertical conductivities are4.5×10⁻⁸/2.0×10⁻⁸ m/s. A transformed square flownet has 6 flow channels and 25 potential drops;downstream face is dry. Find seepage in m³/(day·m),to three decimals.

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Correct answer: 0.030 to 0.032

Explanation

Equivalent conductivity for the transformed section is $K_e=\sqrt{K_hK_v}=3.0\times10^{-8}$ m/s. Hydraulic head is 52−2=50 m. Flownet seepage per unit width is $q=K_eH(N_f/N_d)=3\times10^{-8}(50)(6/25)=3.6\times10^{-7}$ m²/s. Convert by 86400 s/day to **.031 m³/(day·m)** after rounding.

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