Question about calculation of N in column chromatography

[jacko0]

Hello, this is a theoretical exercise, that accepts that we have a symmetrical peak that follows the Gaussian Distribution model. The information given is the column length L=20 cm, the retention volume Vr=185 ml, and the peak width W=83 ml. What needs to be calculated is the number of theoretical plates N, as well as the H.E.T.P. Now, normally when calculating N the units in N=(4tr/W)^2 cancel each other as long as the W matches the time unit of tr.
But in this case with the data present the formula to use would be N= (16L^2)/W^2. My question is how do the units affect the result, which is meant to have no units? Should I convert to SI, does it still not matter and I use the numerical value? Because using ml vs L vs m^3 for W should give a completely different N value, same as keeping the L in cm, vs m, etc.
I will add since it's an exercise not an actual measurements, I am not provided with any additional info like the tm and Vm, or the k' (some of that is meant to be calculated later on), in order to get around that specific N formula.

[cloakcompromise]

Could you share the exact reaction or conditions you’re asking about? That’ll make it easier to give a clear answer.