Physic Labs

Fluid mechanics

Bernoulli's law in a Venturi tube

Connect continuity with Bernoulli: speed rises and pressure falls in the constriction; recognize that friction causes flow-energy losses. Measure pressure, flow speed, and height along the tube, and verify p+ρv2/2+ρgh=constantp + ρv²/2 + ρgh = constant for ideal flow.

High school

⚠ The simulated flow is idealized; real fluid experiments require spill control and securely mounted tubing.

Equipment

  • Horizontal Venturi tube with three pressure taps and flow particles
  • Flow-rate Q and dynamic-viscosity μ sliders; pressure-head readout

Procedure

  1. Observe pressure through the constriction

    Keep viscosity μ low and vary flow rate Q with its slider; compare the pressure tubes at wide and narrow cross-sections. Flow is faster and static pressure lower in the constriction. Increase μ to see total head fall along the stream because of viscous losses; in the ideal frictionless model, p + ρv²/2 + ρgh remains constant. Compare the displayed values with p+ρv2/2+ρgh=constantp + ρv²/2 + ρgh = constant.

  2. Check the continuity equation

    Hold Q fixed and compare the wide and narrow sections using the flow particles; observe the higher speed in the constriction. Use Q = Av to compare the flow rate at both locations and note the speed difference. Compare the displayed values with Q=AvQ = Av.

  3. Compare viscous losses

    Reset the simulation, hold Q, and compare the pressure taps as you raise μ. Observe the head falling along the tube; unlike the ideal case, p + ρv²/2 + ρgh is no longer constant because viscous losses remove mechanical energy. Compare the displayed values with p+ρv2/2+ρgh=constantp + ρv²/2 + ρgh = constant.

Simulation

Experiment history

Daniel Bernoulli set out a connection between pressure and fluid motion in Hydrodynamica (1738), when natural philosophers were seeking mechanical principles for flowing matter. His work related pressure, speed, and elevation through an energy account rather than treating pressure only as a static push. In a tube whose cross-section narrows, continuity says that a steady incompressible flow must move faster through the smaller area to carry the same volume per second. The familiar form p + ρv²/2 + ρgh = constant applies along a streamline for an ideal, incompressible, nonviscous fluid. It explains why static pressure often falls as speed rises, but it is not independent of those assumptions: viscosity, turbulence, pumps, and heat exchange alter the energy balance. The Venturi tube turns the relationship into a practical measurement, while pressure taps reveal where pressure energy becomes kinetic energy or is dissipated. The simulation lets you compare this ideal account with losses as viscosity is increased.

Related physicists

Daniel Bernoulli

Related library topics

The Bernoulli equationThe continuity equation