Soil at a site consists of two layers. The top layer has permeability k units and bottom layer has permeability
5k units. If the thickness of both the layers is equal, then what is the average permeability in the vertical
direction?
-
A.
3k units
-
B.
(5/3)k units
-
C.
(5/6)k units
-
D.
(6/5)k units
Correct Answer:
B. (5/3)k units
Explanation:
When water flows vertically through layered soil, the flow occurs in series, and the average permeability is determined using the weighted harmonic mean of the individual layers.
Given: - Thickness of top layer (H1) = H
- Permeability of top layer (k1) = k
- Thickness of bottom layer (H2) = H (since thicknesses are equal)
- Permeability of bottom layer (k2) = 5kThe formula for average vertical permeability (kv) is:
kv = (H1 + H2) / ((H1 / k1) + (H2 / k2))
Substituting the values:
kv = (H + H) / ((H / k) + (H / 5k))
kv = 2H / (5H / 5k + H / 5k)
kv = 2H / (6H / 5k)
kv = (2H \* 5k) / 6H
kv = 10k / 6
kv = (5/3)k units
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