OpenStax College Physics for AP® Courses, Chapter 12, Problem 6 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. We are going to use Bernoulli's equation to answer what must be true about the potential energy per unit volume of a fluid moving along a fluid path when the pressure and kinetic energy per unit volume are increasing. So we know that pressure two at some second position along this fluid path is greater than pressure one so we are told that pressure is increasing and this term here is the kinetic energy per unit volume term and it's going to be greater in the second position than it is in the first position. So both these terms are bigger than their counterparts on the left side and the two sides have to be equal to each other then that must mean this is compensatingly smaller to make up for the amount by which these two terms exceed their counterparts on the left. So ρgh 2 is less than ρgh 1 and this is the potential energy per unit volume term and so that means the potential energy per unit volume is decreasing because this term has to be less than the potential energy per unit volume in the first position. In part (b), we are told that the pressure along a fluid path increases just as before but now the kinetic energy per unit volume remains constant and what must be true then about the potential energy per unit volume? So this term and this term are the same and P 2 is greater than P 1 and in order for the sides to be equal that must mean that this term has to be less than this term which we say here and that means the potential energy per unit volume is decreasing again in this second scenario.