If the velocity of flow of water through the soil is 0.01 cm/s and the piezometer readings at the end points A and B of soil sample are 10 cm and 5 cm, respectively. The distance between the points A and B is 20 cm. Find the coefficient of permeability of the soil sample.

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  1. 0.25 cm/s
  2. 0.04 cm/s
  3. 4 cm/s
  4. 0.025 cm/s

Answer (Detailed Solution Below)

Option 2 : 0.04 cm/s
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Concept:

Darcy’s Law:- The flow of free water through soil is governed by Darcy’s law. As per this law, for laminar flow through homogenous soil, the velocity of flow (v) is given as

ν = ki

where, k = coefficient of permeability, i = hydraulic gradient

ν = discharge velocity or superficial velocity.

Validity of Darcy’s law:

It is valid when the flow through the soil is laminar. This assumption was based on the fact that there is no head loss associated when the water flows through soil due to formation of turbulent rollers.

For the flow of water through soil, the flow is laminar if Reynold’s number is less than 1.

  • In fine-grained soil, flow is laminar.
  • In coarse-grained soil, the flow becomes turbulent when the size of particles is very large i.e. in gravel range.

 

Calculation:

i = h/l, difference in head = h = 10 - 5 = 5 cm and l is the length of pipe through which the flow(head loss) takes places = 20 cm

i = 5/ 20

v = 0.01 cm/sec

V = k × i

0.01 = 5/20 × k

k = 0.04 cm/sec

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