I am a bit unsure on your question. If you specify the mass flow rate (from the volumetric) you would compute the corresponding pressure drop through the domain. If you are certain of this flow rate, then we would not need to iterate because you know it.

It really depends on what you are trying to model and what known boundary conditions you have. Earlier you stated that you knew the pressure difference, and later added you knew the volumetric flow rate. Mathematically we cannot specify all three (look at the NS equations and BCs closely--it is not possible). A general approach would be take it to model it with two (mass flow & a pressure are the best) and use the third (other pressure) as a validation point. But best approach we cannot exactly say without knowing all the details.