Question

Find the relation between $h_1$, $h_2$, and $h_3$ if, during a variable head permeability test on a soil sample, equal time intervals are noted for the head to drop from $h_1$ to $h_2$ and $h_2$ to $h_3$.

• A. $h_1 = \sqrt{2h}_3$
• B. $h_2 = \frac{h_3}{\sqrt{2}}$
• C. $h_2 = \sqrt{h_1 h_3}$
• D. $h_3 = \sqrt{h_1 h_2}$

Hint:

Remember: For a variable head test, the geometric mean of h1 and h3 gives h2 when time intervals are equal.

Answer 1

The Correct Option is C

In a variable head permeability test, the relationship between heads is given by:
\(h2 = \sqrt{h_1h_3}\)
This is derived from the logarithmic decay of the head, where equal time intervals result in a
geometric mean relationship for successive heads.