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

Step 1: Write down Darcy's equation.
Darcy's Law gives discharge as $Q = K i A$, where $K$ is hydraulic conductivity, $i$ is the hydraulic gradient and $A$ is the cross sectional area.
Step 2: Plug in the numbers.
\[ Q = (2\times10^{-4})(0.02)(0.5) \]
Multiplying these three terms together step by step gives $Q = 2\times10^{-6}\ \mathrm{m^3/s}$.
Step 3: Match this to the options.
This value corresponds to option (A), $2\times10^{-6}\ \mathrm{m^3/s}$, and not to the value listed against option (B) in the given answer key, so the key on this one looks off.
\[ \boxed{Q = 2\times10^{-6}\ \mathrm{m^3/s}} \]