30Q3.2 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 (small-bore) tube is at a height h0above 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 = A1kh/L (main text Equation 3.8) In the small-bore tube, the flowrate is given by the cross-sectional area multiplied by the velocity q=A2v but the velocity v = -dh/dt so q=-A2.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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