To calculate the unknown entrance pressure in a pipe, it can be derived from the depth of the tank, with the pressure at the entrance potentially equating to the pressure at the exit. The discussion highlights that if the height (z) is set at 10 m, the pressure at the water surface can be considered as zero, assuming no head loss (hf = 0). Clarification is needed on the reference points for pressure measurement, whether it's from the pipe entry to exit or from the free surface to the pipe exit. Ultimately, understanding the relationship between the tank depth and pressure is crucial for solving the problem. The pressure at the entrance can be calculated using the established principles of fluid mechanics.