Question

An open-ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having the coefficient of permeability of 10^-2m/sec. The barrel stands on a saturated bed of gravel. The time required for the water level in the barrel to drop by 0.75 m is____ 

1. 58.9 s
2. 75 s
3. 100 s
4. 150 s

Answer 1

Correct Answer - Option 2 : 75 s

Concept:

The coefficient of permeability is given by Darcy's Law

v = k × i

v - Average discharge velocity

k - Coefficient of permeability

i - hydraulic gradient.

The coefficient of permeability can also be defined as the average velocity of flow under unit hydraulic gradient.

When i =1, v = k

\({\rm{Coefficient\;of\;permeability}} = \frac{{{\rm{Drop\;in\;heightof\;water\;level}}}}{{{\rm{Time\;taken}}}}\)

Calculation:

Given:

Drop-in water level = 0.75 m

k = 10^-2 m/s

Using the equation: \({\rm{Coefficient\;of\;permeability}} = \frac{{{\rm{Drop\;in\;heightof\;water\;level}}}}{{{\rm{Time\;taken}}}}\)

\({10^{ - 2}} = \frac{{0.75}}{{{\rm{Time\;taken}}}}\)

⇒ Time taken = 75 s