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Q3.2 Solution
Diagram of falling head permeameter: see main text Figure 3.10
The derivation of the equation follows the main text Section 3.4.2.
At the start of the test (time t=0), the water level in the upper (smallbore) tube is at a height
h
0
above the permeameter outlet. After a general time t, the water level in the upper tube has
fallen to a general height h above the permeameter outlet. Applying Darcy's Law at a general
time t to the soil sample in the large tube,
q = Aki = A
1
kh/L
(main text Equation 3.8)
In the smallbore tube, the flowrate is given by the crosssectional area multiplied by the
velocity
q
=
A
2
v
but the velocity v = dh/dt so
q
=

A
2
.dh/dt
(main text Equation 3.9)
(the negative sign is needed because v has been taken as positive downward, while h is
measured as positive upward)
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 Fall '11
 StuartChalk
 Analytical Chemistry, Addition, main text, main text Equation, permeameter

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