Bernoulli Calculator
The Venturi trade in one card: upstream pressure versus throat pressure for two speeds, with the conservation ledger printed on both sections and a hard refusal when the trade would sell pressure below absolute zero.
Bernoulli Calculator
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What this result does not account for
- Horizontal pipe — the height term cancels
- Ideal fluid along a streamline; friction not priced
In short: Water (density ≈ 998 kg/m³, approximate) slowing the ledger: supply 200,000 Pa, 2 m/s in the pipe, 8 m/s at the throat. The dynamic bill is ½ρv² — 1,996 Pa upstream, 31,936 Pa at the throat — so the throat pressure is P₂ = 200,000 + ½·998·(2² − 8²) = 170,060 Pa. The conservation card shows the same total on both sections: 201,996 = 201,996. That is Bernoulli as bookkeeping: where the stream speeds up, it pays with pressure. Push the throat to 25 m/s and the same arithmetic would demand −109,879 Pa — the page refuses: the stream would cavitate long before the ledger went negative.
Formula
P + ½ρv² + ρgh = constant along a streamline · horizontal: P₂ = P₁ + ½ρ(v₁² − v₂²) · dynamic q = ½ρv²
Bernoulli is an energy ledger kept per cubic metre: pressure is the organised push, the dynamic term is the motion, and the height term is gravity's account. In a horizontal pipe the height cancels and the page shows the bare trade — speed bought, pressure paid. Real pipes leak energy to friction, so the ledger holds along a streamline, not around every elbow.
Worked Example
- Enter the supply pressure and the pipe speed at the wide section.
- Enter the throat speed — the flow-rate page's constriction card computes it from your bore ratio.
- Read the throat pressure and check the ledger card: the two totals must agree.
- Heed the refusal: demand too much speed and the ledger goes below absolute zero — cavitation, not physics.
Defaults: 170,060 Pa at the throat; ledger 201,996 both sides. At 25 m/s the trade refuses (would demand −109,879 Pa).
Strengths & Limits Of This Model
Where this engine is strong
- Conservation ledger printed on both sections
- Refuses negative absolute pressure by name
Where it stops
- No friction, elbow or entrance losses
- Constant density — no compressible flow
Practical Use Cases
Venturi sizing
what a throat costs in pressure
Spray and jet work
speed from pressure, honestly traded
Teaching
energy conservation per cubic metre
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Bernoulli Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Where does the height term go?
The page prices the horizontal trade, where every section shares one elevation and ρgh is a constant on both sides — it cancels. Lifting the pipe moves about 9,806 Pa per metre of water, which is its own arithmetic; here the ledger is speed against pressure only.
Why does faster flow mean LOWER pressure?
Because energy per cubic metre is conserved along the streamline: if the motion term ½ρv² grows, the organised push P must shrink to pay for it. The stream is not sucked faster by low pressure as a cause — the geometry forces the speed and the pressure pays the bill. The ledger card shows both totals agreeing to the digit.
Is dynamic pressure a real pressure I can read?
Only as a difference. A gauge moving WITH the flow (a Pitot sensing) reads the stagnation pressure P + q; a wall tap reads P alone. The difference between those two readings is q — which is exactly how airspeed indicators work.
What is the refusal at the bottom of the ledger?
Absolute zero of pressure. Demand enough throat speed and ½ρv² exceeds the supply, so the arithmetic asks for negative absolute pressure — physically, the water fractures into vapour: cavitation. The page refuses rather than print a negative ledger, and names the number it refused.
Do real pipes obey this to the digit?
No, and the page says so: friction taxes every metre and fittings take bites. Bernoulli holds along a streamline for an ideal fluid; engineers use it as the first word on a trade, then price the losses separately. Treat the computed P₂ as the ceiling the real throat underperforms.
Can I use gauge pressure?
Only consistently, and only if it stays positive: the ledger needs absolute pressures because its refusal floor is absolute zero. A gauge reading of zero is about 101,325 Pa absolute at sea level — quoting the wrong baseline moves every card.
Does this work for air?
The arithmetic does, at low speeds: with density ≈ 1.225 kg/m³ the dynamic terms are small and the trade is gentle. At speeds near or beyond a third of the speed of sound, compressibility breaks the constant-density premise and the page's honest answer is: different equations live there.
How does this connect to the other fluid pages?
As one chain: the flow-rate page gives you Q = A·v and the constriction speed; this page prices that speed in pressure; the Reynolds page warns whether the flow will behave as clean layers or as a mixing churn on the way. Three pages, one pipe.