Question

A soil sample has \(K = 2 \times 10^{-4}\ \mathrm{m/s}\), area \(=0.5\ \mathrm{m^2}\) and hydraulic gradient \(=0.02\). Then discharge \(Q\) is

• A. \(2\times10^{-6}\ \mathrm{m^3/s}\)
• B. \(2\times10^{-5}\ \mathrm{m^3/s}\)
• C. \(2\times10^{-3}\ \mathrm{m^3/s}\)
• D. \(2\times10^{-4}\ \mathrm{m^3/s}\)

Hint:

Remember Darcy's Law: \[ \boxed{Q=KiA} \] Always substitute values carefully while keeping SI units consistent.

Answer 1

The Correct Option is B

Using Darcy's Law, \[ Q=KiA \] Substituting the given values, \[ Q=(2\times10^{-4})(0.02)(0.5) \] \[ Q=2\times10^{-6}\ \mathrm{m^3/s} \] Hence, \[ \boxed{Q=2\times10^{-6}\ \mathrm{m^3/s}} \] Therefore, the correct answer is \[ \boxed{(A)} \] Note: Although the image marks option (B) as correct, applying Darcy's Law with the given values yields \(2\times10^{-6}\ \mathrm{m^3/s}\). Thus, the marked key appears to contain an error.