Energy Conservation in Fluids
Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. It is essentially the grand principle of conservation of energy applied strictly to fluid flow.
The equation proves that the total energy in a steady flow of an incompressible, frictionless fluid remains mathematically constant along a streamline. This total energy is the sum of three distinct components: static pressure (ambient crushing pressure), dynamic pressure (kinetic energy from velocity), and hydrostatic pressure (potential energy from physical elevation).
How Aerodynamics Works
Bernoulli's equation is one of the most famous equations in physics because it fundamentally explains how airplanes fly.
An airplane wing (an airfoil) is precisely shaped so that air travels significantly faster over the curved top surface than it does across the flat bottom surface. According to Bernoulli, this faster-moving air over the top exerts much lower static pressure. The slower-moving air underneath retains higher pressure, physically pushing the wing upward into the lower pressure zone, creating lift.
The Formula
Example Calculation
Calculate the total pressure of water (density $1000 , ext{kg/m}^3$) flowing at $5 , ext{m/s}$ through a pipe at an elevation of $10 , ext{meters}$, assuming a static pressure of $101,325 , ext{Pa}$.
- Dynamic Pressure: $0.5 \cdot 1000 \cdot 5^2 = 12,500 , ext{Pa}$.
- Hydrostatic Pressure: $1000 \cdot 9.81 \cdot 10 = 98,100 , ext{Pa}$.
- Total Pressure: $101,325 + 12,500 + 98,100 = 211,925 , ext{Pa}$.
If the pipe suddenly dropped to an elevation of $0 , ext{meters}$, the hydrostatic pressure would become zero, forcing the velocity or static pressure to drastically increase to maintain the $211,925 , ext{Pa}$ constant.