GATE 2016 CE (CE2) – Question 53
Water flows from P to Q through two soil samples, Soil 1 and Soil 2, having cross sectional area of 80 cm2 as shown in the figure. Over a period of 15 minutes, 200 ml of water was observed to pass through any cross section. The flow conditions can be assumed to be steady state. If the coefficient of permeability of Soil 1 is 0.02 mm/s, the coefficient of permeability of Soil 2 (expressed in mm/s) would be ________ Soil 1 Soil 2 600 mm 150 mm 150 mm 300 mm P Q
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Correct answer: 0.04 to 0.05
Explanation
Discharge is200000mm³/900s and area8000mm², so Darcy velocity is0.0277778mm/s. Head loss through Soil1 is vL1/k1=0.0277778·150/0.02=208.333mm. Total loss is600−300=300mm, leaving91.667mm for Soil2. Thus k2=vL2/Δh2=**0.04545mm/s**.