Bernoulli Equation Calculator

The Bernoulli equation expresses conservation of mechanical energy along a streamline in a moving fluid. It balances static pressure, kinetic energy per unit volume, and gravitational potential energy per unit volume. If a fluid speeds up while remaining at the same elevation, static pressure generally falls. If it flows downward, lost elevation can become pressure or velocity. This calculator rearranges that balance to solve the static pressure at point two. Enter pressure at point one in pascals, both velocities in meters per second, both elevations in meters, and density in kilograms per cubic meter. The calculation uses standard gravitational acceleration of 9.81 meters per second squared. Pressure at point two equals inlet pressure plus one-half density times the difference between squared velocities, plus density times gravity times the elevation drop. Pressure-head values divide each pressure by density and gravity, making the pressure contribution comparable to velocity head and elevation head in meters of fluid. The simple Bernoulli model assumes steady, incompressible, inviscid flow along the same streamline. It also assumes no pump adds energy, no turbine removes energy, and no meaningful friction or fitting loss occurs between the selected points. Those assumptions are often suitable for demonstrations, rough estimates, smooth short passages, and ideal nozzle or tank problems. Real piping systems normally require an extended energy equation that includes pump head, turbine head, and major and minor losses. Use either absolute pressure at both points or gauge pressure at both points; never mix the two reference systems. Density should be appropriate for the fluid and temperature. Water near room temperature is commonly approximated as 1,000 kilograms per cubic meter, while gases may change density enough that an incompressible treatment becomes inaccurate. A negative calculated gauge pressure can indicate suction conditions, but it should also prompt a check for cavitation, vapor pressure, and invalid assumptions. The result is useful for fluid mechanics study and preliminary engineering analysis, but safety-critical pipe, nozzle, and hydraulic designs should be checked with complete loss data and applicable design standards.