Fluid Dynamics - Bernoulli's Principle

An important idea in fluid flow is that of the conservation of mass. This implies that the amount of fluid that goes in through one end of a pipe is the same as the amount of fluid that comes out through the other end. Thus the fluid has to flow faster in narrower sections or constrictions in the pipe. Another important idea, expressed by Bernoulli's principle, is that of the conservation of energy.

Daniel Bernoulli (1700-1782) was the first person to study fluid flow mathematically. He imagined a completely non-viscous and incompressible or "ideal" fluid in order to simplify the mathematics. Bernoulli's principle for an ideal fluid essentially says that the total amount of energy in a laminar flow is always the same. This energy has three components—potential energy due to gravity, potential energy due to pressure in the fluid, and kinetic energy due to speed of flow. Since the total energy is constant, increasing one component will decrease another. For instance, in a horizontal pipe in which gravitational energy stays the same, the fluid will move faster through a constriction and will, therefore, exert less pressure on the walls. In recent years, powerful computers have made it possible for scientists to attack the full mathematical complexity of the equations that describe the flow of real, viscous, and compressible fluids. Bernoulli's principle, however, remains surprisingly relevant in a variety of situations and is probably the single most important principle in fluid dynamics.