For one dimensional flow, what is the flow rate in a 2.0-m long sample of clean saturated sand having a cross-sectional area of 0.05 m2, and a hydraulic conductivity value of 10-3 m/s, if the drop in head over the length of the sand sample is 0.03 m?

To calculate the flow rate in a one-dimensional flow, we need to use Darcy's law, which relates the flow rate to the hydraulic conductivity, cross-sectional area, and the drop in head.

Darcy's law is given by:

Q = (K * A * dh) / L

Where:
Q = Flow rate
K = Hydraulic conductivity
A = Cross-sectional area
dh = Drop in head (change in elevation)
L = Length of the sample

Given:
L = 2.0 m (length of the sand sample)
A = 0.05 m^2 (cross-sectional area)
K = 10^-3 m/s (hydraulic conductivity)
dh = 0.03 m (drop in head)

Substituting the given values into Darcy's law:

Q = (10^-3 m/s * 0.05 m^2 * 0.03 m) / 2.0 m

Simplifying the equation:

Q = 0.0000015 m^3/s

Therefore, the flow rate in the 2.0 m long sample of clean saturated sand is 0.0000015 m^3/s.