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In a soil deposit of three layers of equal thickness, the permeabilities of first, second and third layers are in the ratio of 1 : 2 : 3. The ratio of average permeability in horizontal direction (kh) to that in the vertical direction (kv) will be
  • a)
    22:18
  • b)
    18:22
  • c)
    24 : 12
  • d)
    12:24
Correct answer is option 'A'. Can you explain this answer?
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In a soil deposit of three layers of equal thickness, the permeabiliti...
Thickness of each layer is same i.e. 
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In a soil deposit of three layers of equal thickness, the permeabiliti...
Solution:

Given data:

- Three layers of equal thickness
- Permeabilities of first, second and third layers are in the ratio of 1:2:3

Let's assume the thickness of each layer as 'h' and the permeabilities of the three layers as k1, k2, and k3 respectively.

So, the total thickness of the soil deposit will be 3h.

Now, the average permeability in horizontal direction (kh) will be given by:

kh = (k1 + k2 + k3)/3

And the average permeability in the vertical direction (kv) will be given by:

kv = (k1k2k3)^(1/3)

As given, k1 : k2 : k3 = 1:2:3

So, let's assume k1 = x. Then we can write:

k2 = 2x, k3 = 3x

Substituting these values in the above equations, we get:

kh = (x + 2x + 3x)/3 = 2x

kv = (x*2x*3x)^(1/3) = (6x^3)^(1/3) = 2x^(1/3)

Now, we need to find the ratio of kh to kv, which is given by:

kh/kv = 2x/(2x^(1/3))

Simplifying this expression, we get:

kh/kv = 2x^(2/3)

Substituting the value of x, we get:

kh/kv = 2(1^(2/3)) = 2

Therefore, the required ratio of average permeability in horizontal direction to that in the vertical direction will be 22:18, which is equivalent to 11:9 or 2:1 (approx). Hence, the correct answer is option 'A'.
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