Step 1: Recall what the coefficient of permeability is.
The coefficient of permeability \(k\) (also called hydraulic conductivity) measures how easily water flows through a soil.
Step 2: Write Darcy's law.
Darcy's law states \[ v = k\,i \] where \(v\) is the flow velocity and \(i\) is the hydraulic gradient.
Step 3: Find the unit of each term.
Velocity \(v\) has units of length per time, like cm/s. The hydraulic gradient \(i\) is length divided by length, so it has no unit.
Step 4: Rearrange for k.
From \(v = k\,i\) we get \[ k = \frac{v}{i} \]
Step 5: Work out k's unit.
Since \(i\) has no unit, \(k\) takes the same unit as \(v\), which is cm/s.
Step 6: Conclusion.
The unit of the coefficient of permeability is cm/s.
\[ \boxed{\text{cm/s}} \]