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Premium experiment • continuity + Bernoulli

PHYSICS • FLUID MECHANICS

Bernoulli’s Principle & Venturi Tube

Change pipe geometry and flow conditions to see continuity accelerate fluid through a throat while Bernoulli pressure falls.

● STEADY FLOWContinuity + Bernoulli
Throat velocity
Throat pressure
Pressure drop
Flow rate

Reasoning inspector

live model state
Inlet area A₁—
Throat area A₂—
Area ratio A₁/A₂—
Inlet speed v₁—
Throat speed v₂—
Velocity ratio—
Flow rate Q—
Inlet pressure P₁—
Throat pressure P₂—
Pressure drop ΔP—

Flow through a constriction

For ideal steady incompressible flow at equal elevation, continuity fixes the velocity change and Bernoulli’s equation converts pressure energy into kinetic energy.

LEARN WITH THE SIMULATION

Understand Bernoulli’s Principle & Venturi Tube by experimenting.

START HERE

A Venturi tube links two conservation laws in one flow path. Continuity requires the same steady volumetric flow rate through the wide inlet and narrow throat, so reducing area forces velocity upward. Bernoulli's ideal streamline relation then balances static pressure with kinetic-energy density, producing a pressure drop where the fluid moves faster. The premium lab exposes area ratio, velocity ratio, flow rate and pressure taps together so the causal chain can be checked quantitatively.

BUILD THE IDEA

What you should understand first

  • Use A₁v₁ = A₂v₂ to predict throat velocity from area ratio.
  • Apply Bernoulli's equation at equal elevation to connect a speed increase with a static-pressure decrease.
  • Distinguish constant volumetric flow rate from changing local velocity.
  • Explain how density, inlet speed and throat geometry affect the predicted pressure drop in the ideal model.

TRY IT YOURSELF

Why can the throat velocity increase dramatically even though the number of liters per second stays unchanged?

  1. Hold inlet diameter and inlet velocity fixed while gradually reducing throat diameter.
  2. Compare A₁/A₂ with v₂/v₁ in the inspector.
  3. Verify that A₁v₁ and A₂v₂ represent the same volumetric flow rate.
  4. Watch the pressure taps and compare the resulting pressure drop with the velocity increase.
Read the visual:

A smaller throat area requires a larger local velocity so the same volume passes each cross-section per unit time. At equal elevation in an ideal inviscid flow, that kinetic-energy increase is balanced by a decrease in static pressure.

WHY IT WORKS 01

Area ratio controls velocity ratio through continuity

For steady incompressible flow, conservation of volume gives A₁v₁ = A₂v₂. Therefore v₂/v₁ = A₁/A₂. Because circular area scales with diameter squared, halving the diameter reduces area by a factor of four and ideally raises the velocity by a factor of four, which is more dramatic than reasoning from diameter alone.

WHY IT WORKS 02

Bernoulli converts speed change into pressure change

At equal elevation and without losses, P + ½ρv² stays constant along the modeled streamline. Once continuity determines the throat speed, the pressure follows from P₂ = P₁ + ½ρ(v₁² − v₂²). The pressure taps in the visualization make this energy trade visible instead of presenting pressure drop as an isolated formula.

WHY IT WORKS 03

The model is an ideal benchmark, not a universal pipe law

Real fluids develop boundary layers, turbulence and irreversible pressure loss, especially through sharp contractions and at high Reynolds number. A real Venturi meter is designed to control these effects and uses calibration or discharge coefficients. The simulator intentionally omits those losses so learners can isolate continuity and Bernoulli reasoning before adding engineering corrections.

DO NOT MIX THESE UP

Common misconception

Bernoulli's equation does not say that faster fluid always has lower pressure under every circumstance. Elevation, pumps, turbines, viscous losses and turbulence can change the energy balance. Continuity also does not require equal velocity everywhere; it requires consistent mass or volumetric flow under the assumptions used here.

PRACTICE CHALLENGE

Can you hit a requested pressure drop and explain how the same flow rate produces different local speeds?

  • Choose a pressure-drop target.
  • Adjust throat diameter or inlet speed until the target is reached.
  • Use the inspector to verify that A₁/A₂ equals v₂/v₁ in the ideal calculation.
  • Explain why Q remains the same at both sections while static pressure changes.
Reveal the reasoning

Continuity fixes the same volumetric flow Q at both sections, so shrinking A₂ forces v₂ upward. Bernoulli then predicts a lower P₂ because more of the streamline energy appears as kinetic energy. The pressure target can therefore be reached by changing geometry, speed or density while preserving the same Q through each cross-section.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Flow is steady, incompressible and evaluated along a streamline at equal elevation.
  • Continuity uses A₁v₁ = A₂v₂ with circular pipe areas.
  • Bernoulli pressure change includes only kinetic-pressure exchange and neglects losses.

Model limitations

  • Viscosity, turbulence, cavitation, pump work and elevation changes are omitted.
  • Very large contraction ratios can produce unrealistic ideal speeds and pressure drops compared with real hardware.

CONNECT IT

Where this matters

  • Venturi flow meters
  • Carburetors and aspirators
  • Pipe and nozzle analysis
  • Pressure-based velocity measurement

WORDS THAT MATTER

Key vocabulary

Continuity
Conservation relation requiring consistent steady flow through successive cross-sections.
Volumetric flow rate
Volume per unit time Q = Av for a uniform cross-section.
Static pressure
Thermodynamic pressure excluding the directed kinetic-energy term.
Dynamic pressure
Kinetic-energy density term ½ρv² used in Bernoulli reasoning.
Venturi effect
Pressure reduction associated with acceleration through a constricted passage under suitable flow conditions.