Hydraulics of laminar flow

For laminar flow, poisseulie's derived an expression for discharge through a round capillary tube as :
             K = c x d^2  x (e^3/1+e) x Yw/ų
This is the equation to determine the value of permeability.

#Factors Affecting coefficient of permeability.
• Grain size
• Properties of pore fluid
• void ratio
• structural arrangement of soil particles.
• Entrapted air
● Grain size.
From above equation of determined by k, gou can see k is depend upon the d. That means k is also depends upon the cof. Permeability.
●Properties of pore fluid :
As same that equatio, you can see that k is the function of unit weight and viscosity of pore fluid. For water unit weight is same but viscosity may change with temperature.
● Void ratio.
In the equation of determining the cofficient of permeability, you can see the k is directly propotion to cxe^3/1+e where, c is the independent of k.
●Structural arrangement and soil particles.
From the equation to determine the k
, k is the function of the structural arrangement of soil particles and depends upon method of soil deposition, environment, method of placement(compaction) and stratification.
●Entrapped air :
Presence of entrapped air and other organic impurities obstruct the flow causing reduction of permeability.


# Determination of coefficient of permeability in laboratory:
A) Constant head permeability test :
The experimental set up for constant head test is shown in fig.
Let, A = Area of cross section of soil specimen.
       L = Length of soil sample.
       h = constant head
The constant head h, causing flow is vertical distance between the water levels in overhead and bottom tanks.
After ensuring that the soil specimen is fully saturated and the flow has become steady, the quality of q following through the soil specimen in a found. Applying to darcy law, we have.
             q= kiA
             Q/t = K h/L A
                K = QL/Aht  = qL/Ah
              

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