With a flow rate of one cubic centimeter per second across a cross sectional area of one square centimeter with a fluid of one centipoise viscosity and a pressure gradient at one atmosphere per centimeter of length,
it is obvious that k is unity.
For the units described above,
k has been arbitrarily assigned a unit called Darcy in honor of the man responsible for the development of the theory of flow through porous media.
Thus, when all other parts of Equation 4-39 have values of unity, k has a value of one Darcy.