Applications of Bernoulli's Equation

Venturi effect, aerodynamic lift, Torricelli's theorem, and Pitot tube flow measurements.

General idea of the topic

Bernoulli's equation relates pressure, velocity and height in an ideal flow, and from it come well-known instruments and phenomena. Where the fluid speeds up, the pressure drops; where it slows down, it rises.

The topic applies that idea to three cases: the Venturi effect, in which a constriction lowers the pressure and allows the flow rate to be measured; the Pitot tube, which measures speed from the difference between stagnation and static pressure; and the lift of a wing, where the pressure difference between upper and lower surface produces an upward force.

What you will truly understand

By the end you will be able to compute the flow rate of a Venturi tube, the speed with a Pitot tube and the approximate lift force on a surface.

You will also be able to point out the limits of the ideal model, especially in real lift.

Recommended learning route

1. Venturi Effect: narrowing of the cross-section, pressure drop and flow measurement.
2. Pitot Tube: stagnation pressure versus static pressure and the flow velocity.
3. Lift: pressure difference between the faces of a wing and the resulting force.

Physical criterion you must acquire

The essential criterion is to identify the two points between which Bernoulli is applied and combine with continuity to eliminate one velocity. In the Pitot tube the speed comes from v = √(2Δp/ρ). Explaining lift by Bernoulli alone is incomplete: circulation and angle of attack also matter.

Connection with real problems

• flow meters and carburetors.
• airspeed indicators on aircraft.
• wings, propellers and sails.
• sprayers and water aspirators.

Final goal of the topic

The final goal is to apply Bernoulli and continuity to real instruments and phenomena and recognize how far the ideal model goes.