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Bernoulli Equation Calculator

Compute the total pressure of a flowing fluid at a point with Bernoulli's equation P + ½ρv² + ρgh — enter the pressure, density, velocity and height, in any units, and see each term (static, dynamic, hydrostatic) broken out.

 

Formula

$$ P_{total} = \underbrace{P}_{\text{static}} + \underbrace{\tfrac12\rho v^{2}}_{\text{dynamic}} + \underbrace{\rho g h}_{\text{hydrostatic}} = \text{constant along a streamline} $$

Worked example

Water (ρ = 1000 kg/m³) at 101,325 Pa, flowing at 5 m/s, 2 m high has total pressure \( 101325 + \tfrac12(1000)(5)^2 + (1000)(9.81)(2) = 101325 + 12{,}500 + 19{,}620 \approx 133{,}445\ \text{Pa} \).

How it works

Bernoulli's equation expresses conservation of energy for an ideal (incompressible, frictionless) fluid along a streamline: the sum of the static pressure P, the dynamic pressure ½ρv², and the hydrostatic pressure ρgh stays constant. This calculator adds the three at one point to give the total pressure (the Bernoulli constant).

Because the total is fixed, where a fluid speeds up (higher ½ρv²) its static pressure P must fall — the principle behind aerofoil lift, venturi meters and carburettors. Enter values in any units and the calculator converts to SI, showing how each term contributes.

Frequently asked questions

What is Bernoulli's equation?

Bernoulli's equation states that for an ideal fluid, P + ½ρv² + ρgh is constant along a streamline — static plus dynamic plus hydrostatic pressure stays the same as the fluid flows.

Why does faster-moving fluid have lower pressure?

Because the total P + ½ρv² + ρgh is constant. If velocity v rises, the dynamic term ½ρv² grows, so the static pressure P must fall to keep the sum fixed. This is the Bernoulli effect behind wing lift.

What are the three terms in Bernoulli's equation?

Static pressure P, dynamic pressure ½ρv² (from motion), and hydrostatic pressure ρgh (from height). All three have units of pascals and sum to the total pressure.

What are the assumptions of Bernoulli's equation?

It assumes steady, incompressible, frictionless (non-viscous) flow along a single streamline with no energy added or removed. Real flows with turbulence or viscosity deviate from it.

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