What’s truly known:
At the inlet and outlet, we can measure dry-bulb temperature (Tdb), relative humidity (RH), humidity ratio (w), dry-air mass flow rate (ṁₐ), and water inlet/outlet temperature and flow (ṁw). From these, we can compute the total heat rejected exactly:
Qtotal = ṁₐ (hout − hin) = ṁw cp(Tw,in − Tw,out)

What’s not known inside the tower:
As air rises through the fill, its temperature and humidity change continuously. The interfacial film temperature (T_film), local humidity ratio, and transfer coefficients vary with height. Since we only know the inlet and outlet bulk states, the internal psychrometric path is unknown, different paths can lead to the same outlet point but with different sensible-latent proportions.

Why the split can’t be derived exactly:
The total enthalpy change (Δh) is measurable, but dividing it into sensible and latent parts requires assumptions about film temperature, Lewis number, and the heat–mass transfer path. Any numerical split becomes model-dependent (Merkel, Poppe, CFD) rather than directly measurable. Different models can yield slightly different partitions even for identical data.

Concise truth:
Inside a cooling tower, air does not heat and humidify uniformly. The total energy exchange can be determined precisely, but the sensible–latent split depends on the unknown internal path, hence it can only be estimated through validated models, not derived directly from bulk inlet and outlet conditions.