Calculation of true thickness of the bed

 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)

L2_Darcys_Law.pdf (nmt.edu)