GATE 2026 CE (CE1) – Question 31
For a liquid, the permeability of a sandy soil having a void ratio of 0.60 was determined as 0.14 cm/s. Considering the same liquid and by using Taylor's equation, the permeability (in cm/s) of this soil corresponding to the void ratio of 0.80 is ______ (*rounded off to two decimal places*).
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Correct answer: 0.28 to 0.30
Explanation
Taylor's equation says the permeability is proportional to $\frac{e^3}{1 + e}$. For $e = 0.6$ this is $\frac{0.216}{1.6} = 0.135$, and for $e = 0.8$ it is $\frac{0.512}{1.8} = 0.2844$. So $k = 0.14 \times \frac{0.2844}{0.135} = 0.295$, which is 0.29 to two decimal places.