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Bernoulla

Bernoulli’s Principle Physics

\[P + \tfrac{1}{2}\rho v^{2} + \rho g h = \text{const}\]
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Why does a shower curtain drift inward? Bernoulla follows the flow. Along a streamline in steady, incompressible, frictionless flow, P + ½ρv² + ρgh stays constant, so where the fluid speeds up its pressure drops. It underlies Venturi meters and pitot tubes. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Along a streamline in a steady, frictionless flow, pressure plus kinetic energy per volume plus gravitational energy per volume stays constant. So where the fluid speeds up, its pressure drops.

Bernoulla follows the flow, and she knows where the pressure goes.

Daniel Bernoulli derived his theorem in 1738. Along a streamline in steady flow of a fluid with negligible viscosity and compressibility, pressure plus kinetic energy per volume plus potential energy per volume stays constant. It is energy conservation for an ideal flowing fluid.

So where the fluid speeds up at the same height, its pressure drops. Squeeze water through a narrow section of pipe and it flows faster there, at lower pressure. That is the Venturi effect, and it is how Venturi meters and pitot tubes measure flow.

FAST AIR. LOW PRESSURE. is true along a streamline under those assumptions. It does not mean any fast air is low-pressure: a free jet leaving a nozzle is at the surrounding pressure. And the popular explanation of wings, that air over the top must rejoin air underneath at the same moment, is wrong, as NASA explains.

Bernoulla keeps the books balanced: what the flow gains in speed, it pays for in pressure.

Equations

\[P + \tfrac{1}{2}\rho v^{2} + \rho g h = \text{const}\]
SymbolMeaningUnit
\(P\) static pressure of the fluid \(\mathrm{Pa}\)
\(\rho\) fluid density \(\mathrm{kg/m³}\)
\(v\) flow speed \(\mathrm{m/s}\)
\(g\) gravitational acceleration \(\mathrm{m/s²}\)
\(h\) height \(\mathrm{m}\)

Sources

  1. HyperPhysics — Bernoulli Equation
  2. Encyclopaedia Britannica — Bernoulli’s theorem
  3. NASA Glenn Research Center — Incorrect Lift Theory (equal transit time)

Source Bernoulli, D. (1738). Hydrodynamica, sive de viribus et motibus fluidorum commentarii. Strasbourg: J. R. Dulsecker.

Field notes

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