GATE 2019 CE (CE2) – Question 63
Constant-head tests on specimens S1 and S2 give equal discharge. Height ratio L1/L2 = 1.5, diameter ratio D1/D2 = 0.5 and applied head ratio h1/h2 = 2.0. Find permeability ratio k1/k2.
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Correct answer: 2.95 to 3.05
Explanation
Darcy discharge is $Q=kAh/L$. Equal flows give $$\frac{k_1}{k_2}=\frac{L_1}{L_2}\frac{A_2}{A_1}\frac{h_2}{h_1}=1.5\left(\frac1{0.5}\right)^2\frac12=3.0.$$ Answer **3.0**.