Hydraulics and soil mechanics — unit for coefficient of permeability: In geotechnical and groundwater engineering, the coefficient of permeability (hydraulic conductivity) of soils is generally expressed in which unit?

Introduction / Context:
The coefficient of permeability, also called hydraulic conductivity (symbol k), quantifies how readily water flows through a soil or porous medium under a hydraulic gradient. Choosing the correct unit is fundamental for interpreting laboratory tests (constant-head or falling-head) and for applying Darcy’s law in field problems such as seepage, dewatering, and design of filters and drains.

Given Data / Assumptions:

• We are discussing flow of water through soil under Darcy’s law conditions.
• Permeability k multiplies hydraulic gradient i to give specific discharge (Darcy velocity) q: q = k * i.
• Hydraulic gradient i is dimensionless (head loss per length).

Concept / Approach:
Since q has the dimensions of velocity (volume flux per unit area), k must also have dimensions of velocity. Therefore, its unit must be a length per time. In common geotechnical practice (especially in older texts and many lab reports), centimetre–second units are used, so k is expressed in cm/s (alternatively m/s in SI). Units involving area per time (e.g., cm^2/s) are incorrect for k; those belong to diffusivity-type parameters, not to hydraulic conductivity.

Step-by-Step Solution:

Verification / Alternative check:
Laboratory constant-head test equations give k in terms like (Q * L) / (A * h * t), which reduce to length/time, confirming cm/s (or m/s) as correct.

Why Other Options Are Wrong:

• cm/min: dimensionally acceptable but not the standard reporting unit; most references and correlations use cm/s or m/s.
• cm^2/s and cm^2/min: incorrect dimensions (area/time) and do not match Darcy’s law.
• m^3/s per m^2: although equivalent to m/s, it is not the customary way soils labs report k; the question asks what it is “generally expressed in”.

Common Pitfalls:
Confusing hydraulic conductivity (L/T) with hydraulic diffusivity (L^2/T); mixing m/s and cm/s without unit conversion; reporting “permeability” as a dimensionless percentage.

Final Answer:
cm/s