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GATE 2022 MN – Question 32

Geomechanics and Ground Control · Geomechanics · 1 mark · Numerical answer

Water seeps through a vertical sand column of area 4000 mm² and length 300 mm. Applied head is 600 mm and discharge is 100 mm³/min. Find hydraulic conductivity in mm/min, to three decimals.

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Correct answer: 0.012 to 0.013

Explanation

Darcy’s law is Q=kAi. The hydraulic gradient is head loss/length=600/300=2. Hence k=100/(4000×2)=0.0125 mm/min, rounding to 0.013 mm/min. Use the supplied head as the hydraulic-head difference across the column.

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