Engineering calculator reviewed for preliminary design use · Last updated: March 2026
Apply the Bernoulli equation P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ + ΔP_L to calculate pressure, velocity, or elevation between pipe cross-sections. Apply to nozzle design, orifice sizing, and tank drainage estimation.
Bernoulli Equation Calculator
Bernoulli's theorem is a fundamental principle of fluid mechanics stating that the sum of pressure energy, kinetic energy, and potential energy is conserved along a streamline. The extended form includes head loss for real fluids.
Bernoulli Equation
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ + ΔP_L
P: Static pressure [Pa]
ρ: Fluid density [kg/m³]
v: Flow velocity [m/s]
g: Gravitational acceleration 9.81 [m/s²]
h: Height above datum [m]
ΔP_L: Pressure head loss [Pa]
Applications
Nozzle and orifice velocity/flow rate calculations
Bernoulli's equation applies to steady, incompressible flow along a streamline. For real piping, add a head loss term (ΔPL) for friction. It does not apply to compressible flow, unsteady flow, or flow across shock waves.
What is the relationship between Bernoulli and pressure loss?
The extended Bernoulli equation includes a head loss term: P₁ + ½ρv₁² + ρgz₁ = P₂ + ½ρv₂² + ρgz₂ + ΔPL. The ΔPL term represents energy dissipated by friction and is calculated using Darcy-Weisbach or similar methods.
These results are preliminary estimates for screening-level design use. They do not replace detailed engineering, code compliance verification, or vendor-certified calculations.