Dilution time will strongly depend on the volume of solution and agitation intensity. There is no simple equation which can cover all scenarios and configurations. Depending on volume and agitation, this can be a matter of seconds (small volumes, high agitation) or hours or days (big ponds without agitation) till solution concentration is equal in all points.
One thing I can think of is to monitor dilution temperature. If you add known quantity of NaOH to a known volume of water at given temperature, you can easily calculate the resultant temperature rise of the solution, by using value of enthalpy of dilution.
Dejan IVANOVIC
Process Engineer, MSChE