Detailed modeling is required

Offering extra earnings. There is a product (probe) that is immersed in a heated metal to a liquid state. Gas is being fed into the probe. In the submerged part of the probe there are 2 holes. Through the lower hole flows metal, at the level of the second hole, the pressure of the metal should be compensated by the pressure of the gas supplied inside the probe.
It is necessary to create a detailed model that would describe the processes during immersion to calculate the optimal gas pressure depending on the depth of immersion, the size of the holes, the type of metal (taking into account different surface tension).
Knowledge of physics, thermodynamics, hydrodynamics, gas dynamics will be required