A soil sample, 20 cm^{2 }in cross-sectional area and 10 cm long is tested for permeability in a variable head permeameter. The stand pipe has a cross-sectional area of 1 cm^{2 }and the head drops from 30 cm to 10 cm in 6 minutes and 20 seconds. The soil permeability will be:

This question was previously asked in

HPPSC AE Civil 2016 (HPPTCL) Official Paper

Option 1 : 1.44 × 10^{-3} cm/sec

__Concept:__

Falling head permeability test or variable head permeability test

Coefficient of permeability, \(\rm{k = \frac{{2.303 \times a \times L}}{{A \times t}}{\log _{10}}\left( {\frac{{{h_1}}}{{{h_2}}}} \right)}\)

Where

a = Area of the tube in m2

A = Area of the sample in m2

t = time in seconds

L = length in meter

h1 = initial head at t = 0 sec

h2 = head after ‘t’ time

**Calculation:**

Given,

Area of the stand pipe (a) = 1 cm^{2} and Area of soil sample (A) = 20 cm^{2}

length (L) = 10 cm, time (t) = 6 min 20 sec = 380 second

h_{1} = 30 cm, h_{2} = 10 cm

Coefficient of permeability, \(\rm{k = \frac{{2.303 \times a \times L}}{{A \times t}}{\log _{10}}\left( {\frac{{{h_1}}}{{{h_2}}}} \right)}\)

\(k = \frac{{2.303 \times 1 \times 10}}{{20 \times 380}}\log \left( {\frac{{30}}{{10}}} \right)\)

**k = 1.44 × 10-3 cm/sec**