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UPSC Civil Service Exam Questions - Engineering

Q1:

Soil at a site consists of two layers. The top layer has permeability k units and bottom layer has permeability 5k units. If the thickness of both the layers is equal, then what is the average permeability in the vertical direction ?

A 3k units

B (5/3)k units

C (6/5)k units

D (5/6)k units

ANS:B - (5/3)k units

Given,

H1 = H, K1 = K
H2 = H, K2 = 5K
Kave = ?
Kave = (H1 + H2)/(H1/K1 +H2/K2)
= (H+H)/(H/K+H/5K)
= 2/(1/K+1/5K)
= 2/(6/5K)
=(5/3)K.