# Derivation of Bernoulli's Equation

In the derivation of Bernoulli's equation through conservation of energy, as shown in http://www.4physics.com/phy_demo/bernoulli-effect-equation.html, the net work done on a section of fluid is calculated and equated to the change in its mechanical energy. According to the site, two forces do work on the fluid; namely, an external force $F_1$ driving the fluid forward, and a force $F_2$ exerted at the right end of the fluid. How is the force $F_2$ exerted on the fluid, and why is it directed opposite to the motion?

The forces are provided by the pressure of fluid further on. The force $F_1$ is caused by the pressure of the fluid 'behind' the body of fluid considered, the force $F_2$ is caused by the fluid 'ahead' pushing back. Pressure is an internal force for a fluid, any surface within a fluid volume will have the force of pressure acting across it.

• Right. It's just F=ma for an infinitesimal volume. And F=ma conserves both momentum and kinetic energy. – Mike Dunlavey Nov 29 '17 at 16:28