## Co-efficient of Permeability by Falling Head Permeameter

This test is suitable for fine grained soils.

The apparatus used for this test is called falling head permeameter.

The soil sample is kept in a vertical cylinder of cross sectional area A and length L .A transparent stand pipe sectional area a is attached to the test cylinder.

The test cylinder is kept in a container
filled with water of constant level. the soil sample is saturated by allowing
the water to flow through the sample continuously.After the saturation is
complete, the stand pipe is filled with water and the water is allowed to run down and a stop watch is started.

The head at any time instant 't' is equal to the
difference in the water level in the stand pipe and the bottom tank. Let h1 and h2 be the heads at time interval t1 and t2 (t2>t1)respectively.
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Let 'h' be the head at
any intermediate time interval 't' and dh be the change in the head in 'a' smaller
time interval dt . Hence, from Darcy's
law ,the rate of flow q is given by.

q = (- dh.a )/dt = K.i.A

[minus sign has been used since 'h' decrease as 't' increase]

where m i = Hydraulic gradient at time 't' = h/L

K.h.A/L = -dh.a /dt

or, A.K.dt/a.L = -dh/h

Integrating between two time limits, we get