Question

The dimension of permeability is

• A. $L$
• B. $L^2$
• C. $L^3$
• D. $L^2T^{-2}$

Hint:

Remember: Permeability is a property of the porous medium only and always has the dimension of area ($L^2$).

Answer 1

The Correct Option is B

Step 1: Understanding permeability.
Permeability in soil mechanics or hydrogeology refers to intrinsic permeability ($k$). It describes the ability of a porous medium to transmit fluids and is a property of the medium only, independent of the fluid. Step 2: Dimensional analysis from Darcy's law.
Darcy's law states: \[ v = \frac{k}{\mu} \, \Delta P \] where: - $v$ = superficial velocity $\left[ LT^{-1} \right]$
- $k$ = permeability $\left[ ? \right]$
- $\mu$ = dynamic viscosity $\left[ ML^{-1}T^{-1} \right]$
- $\Delta P$ = pressure gradient $\left[ ML^{-2}T^{-2} \right]$ Step 3: Isolating $k$. From Darcy's law: \[ k = \frac{v \, \mu}{\Delta P} \] Substituting dimensions: \[ k = \frac{\left[ LT^{-1} \right] \cdot \left[ ML^{-1}T^{-1} \right]}{\left[ ML^{-2}T^{-2} \right]} \] Simplifying: \[ k = \frac{[ M^1 L^0 T^{-2} ]}{[ M^1 L^{-2} T^{-2} ]} \] \[ k = [ L^2 ] \] Step 4: Conclusion. The dimension of permeability is: \[ \boxed{L^2} \]