Question

For a sheet pile wall constructed in a soil having effective grain size = 0.1 mm, the difference of the upstream and downstream water levels is 3 m. If the flow net drawn for the problem yields 2 as the ratio of number of head drops to number of flow channels, then what is the discharge in unit of m${}^3$/s /m length of sheet pile wall?

• A. $3.0\times {10}^{-4}$
• B. $3.0\times {10}^{-2}$
• C. $1.5\times {10}^{-4}$
• D. $1.5\times {10}^{-2}$

Answer 1

The correct option is C $1.5\times {10}^{-4}$

The permeability of a soil as per Hazen equation is given by

$k=100D_{10}^2$ in cm/s

where $D_{10}$ is Hazen's effective grain size in cm.

$\therefore$ $k=100\times {\left(\frac{0.1}{10}\right)}^2$

$=0.01cm/s$

$={10}^{-4}m/s$

The discharge per unit length is given by

$q=k\times H\times \frac{n_f}{n_d}$

$={10}^{-4}\times 3\times \frac{1}{2}$

$=1.5\times {10}^{-4}{m}^3/s/m$