Bernoulli’s Principle, explained.
Bernoulli’s principle balances pressure, kinetic and gravitational energy along a streamline under specified ideal-flow conditions.
Why it happens
Fixed volume flow makes velocity inversely proportional to cross-section area. At equal height, pressure difference is half the water density times the difference in squared speeds.
Bernoulli’s principle balances pressure, kinetic and gravitational energy along a streamline under specified ideal-flow conditions.
Read the result
The same selected volume flow passes both sections. The higher local velocity comes from smaller area, with pressure changing to preserve the ideal energy balance.
A worked example
A constriction at fixed volume flow
Set volume flow to one litre per second with first area four square centimetres.
Set second area to one and compare speeds 2.5 and ten metres per second.
Read second pressure about 353.13 kPa, below the initial four hundred, under the equal-height ideal assumptions.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Fixed volume flow makes velocity inversely proportional to cross-section area. At equal height, pressure difference is half the water density times the difference in squared speeds.
Where this idea is useful
A practical use
Distinguish a faster stream in a constriction from an increase in static pressure.
A common misconception
“Faster fluid must have higher static pressure everywhere.”
In this ideal horizontal streamline comparison, increased kinetic energy accompanies lower static pressure; added pumps or losses change the balance.
What this explanation leaves out
- Steady incompressible inviscid flow without pumps is assumed. Geometry is schematic; turbulence, friction and energy losses are not predicted.
Does the pipe’s drawn height measure cross-section exactly?
No. The pipe is schematic; numerical areas and calculated velocities define the model, not the two-dimensional illustration.
Are flow rate, velocity and pressure being treated as distinct quantities?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.