Bernoulli's Equation

Bernoulli’s equation says that, for an ideal fluid flowing steadily along one streamline, pressure energy, kinetic energy, and gravitational potential energy can trade off without the total changing. It comes from conservation of mechanical energy applied to a tiny moving fluid element, assuming the fluid is incompressible, inviscid, and not being driven by pumps or losing energy to friction. In practice, faster flow usually means lower static pressure unless the fluid also drops in height or gains energy from outside.

Use this for steady flow in pipes, nozzles, Venturi tubes, tank drains, and airflow over objects when the fluid can be treated as nearly incompressible and losses are small. It is especially useful for finding an unknown pressure, speed, or height difference from measurements at two points on the same streamline.

• Using Bernoulli across two points on different streamlines when the flow is not uniform
• Forgetting that the formula assumes the fluid is incompressible and losses from viscosity are negligible
• Mixing up pressure units or neglecting the height term when the points are at different elevations