The velocity of underground water can be determined by the following formulae:
(A) Slichter’s Formula:
where v = velocity of ground water flow in m/day
k’ = a constant, whose value is approx. 400
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S = slope of the hydraulic gradient line
D10= effective size of the particles in the aquifer
µ = dynamic viscosity of water depending on the temperature.
(B) Hazen’s Formula:
where k” = a constant whose value is approx. 1000
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T = temperature in °C
v, Sand D have the same meaning as in Slichter’s formula.
(C) Darcy’s Law:
It states that the velocity of flow in the laminar range is proportional to the rate of loss of head or hydraulic gradient (h)
After doing long research, it was proved by Darcy that flow of water in soils obey this law. As the head loss is also known as potential loss.
Where K = Darcy’s coefficient of permeability of the soil
V = Velocity of the underground water
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A = Total area
S = Slope of the Hydraulic gradient line.
From the above, it can be assumed that
Where AV = Area of voids through which water percolates
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VP = Actual velocity of percolation
p = Porosity of the soil
Thus the actual velocity of percolation can be determined by dividing the value of V (obtained by Darcy’s law) by the Porosity p.
Example:
Determine the ground water velocity from the following data using Slichter and Hazen’s formulae.
Slichter’s constant =100
Hazen’s constant = 1000
Effective size of the particle in the aquifer = 0.15 mm
Hydraulic gradient = 1 in 100
Viscosity coefficient at 15° C =1.0
Solution:
(i) Using Slichter’s Formula:
(ii) Using Hazen’s formula:
