Bernoulli Equation Calculator

• •Use the Bernoulli Equation Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Bernoulli Equation Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Solve for any unknown in the Bernoulli equation given pressure, velocity, and elevation at two points All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

Bernoulli's equation expresses conservation of mechanical energy for an incompressible, steady, inviscid, and irrotational flow along a streamline: P + ½ρV² + ρgz = constant, where P is static pressure, ρ is density, V is velocity, g is gravitational acceleration, and z is elevation above a reference datum. The three terms represent pressure energy per unit volume, kinetic energy per unit volume, and potential energy per unit volume. The sum is the total mechanical energy per unit volume, which is constant along a streamline in an ideal fluid with no friction, no heat transfer, and no shaft work. Applying Bernoulli's equation between two points 1 and 2 on the same streamline: P₁ + ½ρV₁² + ρgz₁ = P₂ + ½ρV₂² + ρgz₂. This allows solving for any unknown (pressure, velocity, or elevation) given the other five values. The equation is exact for ideal flow and is a good approximation for real flow at high Re (low viscous effects) and over short distances where friction losses are small. For real flow with friction, head loss h_L is added to the downstream side: P₁/ρg + V₁²/(2g) + z₁ = P₂/ρg + V₂²/(2g) + z₂ + h_L. This form is sometimes called the energy equation and is used in hydraulics for pipe networks and open channels. Bernoulli's equation is one of the most widely applied results in fluid mechanics and is the basis for airspeed indicators (pitot tubes), Venturi flow meters, airfoil lift analysis, and siphon flow.

• •Pitot tube airspeed measurement: a pitot tube facing the flow measures stagnation pressure (P + ½ρV²); a static port measures P. The difference is ½ρV², from which velocity is computed: V = √(2·ΔP/ρ). This is the principle behind aircraft airspeed indicators.
• •Venturi flow meter: a Venturi or orifice plate creates a pressure drop at a constriction in a pipe. Bernoulli's equation relates the pressure difference to the velocity at the throat, and from that to the volumetric flow rate.
• •Tank drainage (Torricelli's law): water draining from a tank through a hole in the bottom accelerates to V = √(2gh), where h is the head above the hole. This is Bernoulli's equation applied between the free surface and the hole exit.
• •Airfoil lift analysis: above a wing, air speeds up relative to below, so pressure above is lower than below (Bernoulli). The pressure difference times wing area gives the lift force. This explanation is slightly simplified but captures the essential physics.
• •Water fountain and jet trajectories: the initial velocity of a water jet from a fountain nozzle comes from the pressure head (Bernoulli converting pressure to velocity). Subsequent projectile motion sets the trajectory and height.