GATE CE 2023 Set 2 — Question 60
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Geotechnical Engineering → Permeability → Darcy's Law
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Question
For the flow setup shown in the figure (not to scale), the hydraulic conductivities of the two soil samples, Soil 1 and Soil 2, are mm/s and mm/s, respectively. Assume the unit weight of water as kN/m and ignore the velocity head. At steady state, what is the total head (in m, rounded off to two decimal places) at any point located at the junction of the two samples? ___________________________
Correct answer
4.5 to 4.6
Solution
1.Determine Total Head at Boundaries:
- At the top water surface (elevation m), a pressure of kPa is applied.
- At the bottom water level (elevation m), the total head is m (assuming datum at m and atmospheric pressure).
- Since there is only water between m and m, the total head at the top of Soil 1 (elevation m) is m.
- Since there is only water between m and m, the total head at the bottom of Soil 2 (elevation m) is m.
For steady-state flow through soils in series, the velocity is constant:Given: mm/s, mm/s, m, m.
3.Calculate Head Losses:
Total head loss m.4.Total Head at Junction:
The junction is at the bottom of Soil 1 (elevation m).Total Head at junction m.Rounding to two decimal places, the total head is m.
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