What is the relationship between pressure and flow of pipe flow?
It is a very complicated function, but in general, increase in pressure drop across a section of pipe flow increases the mass flow rate of the fluid. In the laminar flow regime, it is a perfect proportionality, and you can take the electricity hydraulic analogy in reverse, defining an equivalent hydraulic viscous resistance of the pipe section and the fluid flavor. Flow rate is directly proportional to pressure drop In the turbulent flow regime, much more complicated phenomena come in to play. There exist models, but they are based partially on standardized experimental results, instead of on pure physical basis. When the flow is turbulent enough, mass flow rate is proportional to the square root of the pressure drop.
