18. A constant-head permeability test was performed on a vertical sand column of height 40 cm and a cross-sectional area of $25 cm^2$. During the test, when the loss of head was 50cm, the volume of water collected in 2 minutes was $300 cm^3$. Appling Darcy’s law, the calculated coefficient of permeability of the sand column is____________cm/sec [round off to 2 decimal places]
Solution:
Cross sectional Area $(A)=25
cm^2$
Volume of water $(V)= 300
cm^3$
Time $(t)=2 minutes=120
seconds$
i- hydraulic gradient
=$\frac{dh}{dl}$
q-rate of water flow (or)
Rate of discharge= $\frac{Volume}{time}=\frac{V}{t}$
Hydraulic conductivity
(or) coefficient of permeability k=?
Formula,
$q=kA\frac{dh}{dl}$
$k=\frac{q}{A}\frac{dl}{dh}$
We know that $q=\frac{Volume}{time}=\frac{V}{t}$
$k=\frac{V}{t \times
A}\frac{dl}{dh}$
$k=\frac{300}{120\times
25}\frac{40}{50}$
$k=0.1 \times 0.8$
$k=0.08 cm/sec$
Reference: How to Determine Co-efficient of Permeability of Soil? | Soil Engineering (soilmanagementindia.com)
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