Question

The unit of coefficient of permeability is

• A. \(\mathrm{m^2}\)
• B. \(\mathrm{m/s}\)
• C. \(\mathrm{N/m^2}\)
• D. \(\mathrm{kg/m^3}\)

Hint:

Darcy's Law: \[ \boxed{ Q=k\,i\,A } \] where the SI unit of \[ \boxed{k=\mathrm{m/s}.} \]

Answer 1

The Correct Option is B

Step 1: Recall what the coefficient of permeability tells us.
It is also called hydraulic conductivity, written as $k$, and it describes how easily water can move through a soil or rock under a given hydraulic gradient.
Step 2: Use Darcy's law to fix the units.
Darcy's law states $v = k i$, where $v$ is a velocity (length per time) and $i$ is the hydraulic gradient, a pure ratio with no units. Since $i$ has no units, $k$ must carry the same units as $v$.
Step 3: Check the remaining choices.
$\mathrm{m^2}$ describes area, $\mathrm{N/m^2}$ describes pressure, and $\mathrm{kg/m^3}$ describes density. None of these can equal a velocity, so they are ruled out.
\[ \boxed{\mathrm{m/s}} \]