Average number of moles:

This fraction is equivalent to average number of moles of a solute in the mobile phase at any instant divided by the total number of moles of the solute in the column.

v = u ×   Moles of the solute in mobile phase/ Total moles in the column

A number of moles of the solute in the mobile and stationary phases is the product of their concentration and respective volumes

v = u × C _M V_M/(C _M V_M   + C _S V_S)

where, C and V denote the concentration and volume, correspondingly

v = u × 1/(1 + C _S V_S /C _M V_M)

We know that K =  C _S/C _M

Thus, we have a relation between solute migration and distribution constant

v = u × 1/(1 + KV_S /V_M)