Bernoulli equation calculator
Pressure at the second section of a flow from speeds and heights, with the total head.
Fill in the fields and the result will appear here automatically.
Find absolute pressure at a second section of an ideal incompressible flow. Both points belong to one streamline; speeds are nonnegative, density constant, and heights share a datum. Pumps, turbines and losses are not entered. The terms and “total head” are shown in kPa as energy per volume; head in metres would require division by ρg.
How it works
Formula and logic
p₂ = p₁ + ½ρ(v₁² − v₂²) + ρg(h₁ − h₂); the total head sums the static, dynamic and elevation terms. Steady flow along one streamline, constant density, no viscous losses or external machinery. Pressures here are absolute, so a negative result is rejected. Vapour pressure, liquid temperature and cavitation margin are not computed; the energy sum depends on the height datum.
Example
Accelerating water from 2 to 6 m/s at 300 kPa drops the pressure to 284 kPa.
Fields and units
- Pressure at section 1 — kPa
- Speed at section 1 — m/s
- Height of section 1 — m
- Speed at section 2 — m/s
- Height of section 2 — m
- Fluid density — kg/m³
How to use
- — Heights are measured from any common datum: only their difference matters, so either section may be called zero.
- — Find absolute pressure at a second section of an ideal incompressible flow. Both points belong to one streamline; speeds are nonnegative, density constant, and heights share a datum. Pumps, turbines and losses are not entered. The terms and “total head” are shown in kPa as energy per volume; head in metres would require division by ρg.
- — Viscosity is not included: for a long pipe the friction losses must be added on top.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: energy along a streamline
- Limitation
- Steady flow along one streamline, constant density, no viscous losses or external machinery. Pressures here are absolute, so a negative result is rejected. Vapour pressure, liquid temperature and cavitation margin are not computed; the energy sum depends on the height datum.
FAQ
Why does pressure drop in a constriction?
Because the flow is faster there while the total head is conserved: the extra dynamic term can only come out of the static pressure. It contradicts the everyday intuition about squeezing, but any manometer on a Venturi tube confirms it.
Is friction included?
No. Bernoulli's equation is ideal: in a real pipe part of the head goes into friction and local resistances, and over long runs that loss dominates. It is computed separately.
What does a negative pressure in the answer mean?
It is incompatible with the absolute pressure scale and ideal conditions used here. Negative gauge pressure can exist, but this form expects absolute pressure. A cavitation conclusion requires vapour pressure at the liquid temperature and actual losses; neither is supplied.
Does the equation work for gases?
Only when density changes are negligible in the process being considered. The calculator does not check that condition or impose a universal speed threshold. Significant compressibility, shock waves or heat exchange need a different model.