Question

In a falling head permeameter test on a fine sand the sample had a diameter of 76 mm and a length of 152 mm with a stand-pipe of 12.7 mm diameter. A stop watch was started when h was 508 mm and read 19.6 s when h was 254 mm; the test was repeated for a drop from 254 mm to 127 mm and the time was 19.4 s.

Determine an average value for k in m/s.

Answer 1

The average permeability coefficient (k) for the fine sand in the falling head permeameter test can be calculated using Darcy's law for permeability adapted to a falling head setup. The average value of k is found by averaging the permeability values obtained from two separate tests using the provided sample dimensions, stand-pipe dimensions, initial and final head pressure heights, and time intervals.

Step-by-step explanation:

To calculate the average permeability coefficient (k) in m/s for the fine sand in the falling head permeameter test, we use Darcy's law for permeability in the context of a falling head permeameter. The formula is given as:

k = (L/A) * (a/A) * (ln(h0/h1) / t)

where k is the permeability, L is the length of the sample, A is the cross-sectional area of the sample, a is the cross-sectional area of the stand-pipe, h0 and h1 are the initial and final head pressure heights in the stand-pipe, respectively, and t is the time for the head to drop from h0 to h1.

Let's calculate the permeability using the provided data:

First test:

L = 152 mm

Diameter of sample, D = 76 mm, A = π(D/2)^2

Diameter of stand-pipe, d = 12.7 mm, a = π(d/2)^2

h0 = 508 mm, h1 = 254 mm

t = 19.6 s

Second test:

h0 = 254 mm, h1 = 127 mm

t = 19.4 s

The average k can then be calculated by averaging the permeability values obtained from the two tests.