Question

In a falling head permeability test on a soil, the time taken for the head to fall from $h_0$ to $h_1$ is t. The test is repeated with same initial head $h_0$, the final head h' is noted in time t/2. Which one of the following equations gives the relation between h'. $h_0$ and $h_1$?

• A. $h^{\prime }=h_0/h_1$
• B. $h^{\prime }=\sqrt{h_0/h_1}$
• C. $h^{\prime }=h_0{h}_1$
• D. $h^{\prime }=\sqrt{h_0{h}_1}$

Answer 1

The correct option is D $h^{\prime }=\sqrt{h_0{h}_1}$

In falling head permeability test

$k=2.3\frac{aL}{At}lo{g}_{10}\left(\frac{h_0}{h_1}\right)$

$=2.3\frac{aL}{A\left(t/2\right)}lo{g}_{10}\left(\frac{h_0}{h^{\prime }}\right)$

$\therefore$ $lo{g}_{10}\left(\frac{h_0}{h_1}\right)=2lo{g}_{10}\left(\frac{h_0}{h^{\prime }}\right)$

$\Rightarrow$ $\frac{h_0}{h_1}={\left(\frac{h_0}{h^{\prime }}\right)}^2$

$\Rightarrow$ $h^{\prime }=\sqrt{h_0{h}_1}$