Name: bernoulli’s equation in streamlined flow
Uploaded: 2025-05-22T09:06:09.000Z
Duration: 1 min 16 s
Channel: JoVE

Supponiamo un fluido laminare incomprimibile allo stato stazionario che passa attraverso un tubo a sezione trasversale non uniforme.
Poiché il fluido è incomprimibile, il volume dell'elemento fluido e la sua massa rimangono costanti.
La velocità dell'elemento fluido che entra ed esce dal tubo è diversa, con conseguente variazione netta dell'energia cinetica.
La forza che agisce sull'elemento fluido è dovuta alla pressione circostante del fluido.
Quindi, il lavoro netto svolto sull'elemento fluido dal fluido circostante durante lo spostamento è la differenza tra il lavoro svolto durante l'ingresso e l'uscita dal tubo.
Quando l'elemento fluido attraversa la regione elevata, guadagna energia potenziale gravitazionale e viene determinata la variazione dell'energia potenziale gravitazionale.
Secondo il teorema dell'energia cinetica del lavoro, il lavoro netto svolto sull'elemento fluido è uguale alla variazione dell'energia cinetica.
Dividendo per un valore comune, si ottiene un'equazione.
Lungo una linea di flusso, l'energia totale per unità di volume di un fluido che scorre è una costante, chiamata equazione di Bernoulli.

<ol>
	<li>Young, H.D e Freedman, R.A. (2012). Fisica universitaria con fisica moderna. San Francisco, CA: Pearson: sezione 12.5; pagine 385-386.</li>
	<li>OpenStax. (2019). Fisica universitaria Vol. 1. [Versione web]. Estratto da <a href="https://openstax.org/books/university-physics-volume-1/pages/1-introduction">https://openstax.org/books/university-physics-volume-1/pages/1-introduction</a>: sezione 14.6; pagine 716-718.</li>
</ol>

conservazione dell'energia ed equazione di bernoulli

Applicando il principio di conservazione dell'energia o il teorema lavoro-energia a un fluido incomprimibile, privo di viscosità, in flusso laminare, stazionario e irrotazionale, si giunge all'equazione di Bernoulli. Essa afferma che la somma della pressione del fluido, dell'energia potenziale e dell'energia cinetica per unità di volume è costante lungo una linea di flusso.

Tutti i termini dell'equazione hanno le dimensioni dell'energia per unità di volume. L'energia cinetica per unità di volume è chiamata densità di energia cinetica, mentre l'energia potenziale per unità di volume è chiamata densità di energia potenziale.

È importante notare che la densità del liquido non dovrebbe cambiare attraverso il flusso; cioè, dovrebbe essere incomprimibile. Il flusso dovrebbe anche essere laminare e non turbolento. L'equazione di Bernoulli è applicabile ai gas che hanno effetti di compressibilità trascurabili. Per tali gas, la densità è considerata costante e trattata come un fluido incomprimibile. Poiché i gas sono generalmente comprimibili, l'equazione non si applica a essi.

Nonostante sia una semplice riformulazione del principio di conservazione dell'energia con alcune assunzioni critiche, l'equazione rende facile calcolare la pressione in diversi punti se le velocità sono note.

Conservazione dell'energia ed equazione di Bernoulli

L'applicazione del principio di conservazione dell'energia o del teorema dell'energia del lavoro a un fluido incomprimibile e invisibile in un flusso laminare, stazionario e irrotazionale ...

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energy-conservation-and-bernoulli-s-equation

Education

Didattica

JoVE Core

Physics

Fisica

Unit 1

Unità 1

Fluid Mechanics

Meccanica dei Fluidi

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Energy Conservation and Bernoulli's Equation

bernoulli’s equation in streamlined flow

Bernoulli’s equation describes energy in a moving fluid. It comes from the conservation of energy principle, or the work-energy theorem, applied to an incompressible, inviscid fluid in laminar, steady, irrotational flow.

The equation says that pressure energy, potential energy, and kinetic energy per unit volume stay constant along a streamline. Each term has the units of energy per unit volume. The kinetic energy per unit volume is called kinetic energy density, and the potential energy per unit volume is called potential energy density.

The fluid must keep the same density as it flows, so it must be incompressible. The flow also needs to be laminar, not turbulent. Bernoulli’s equation can also apply to gases when compressibility effects are negligible. In that case, the gas density is treated as constant and the gas is handled like an incompressible fluid.

Because gases are usually compressible, the equation does not apply to them in many situations. Even with these limits, Bernoulli’s equation is useful for finding pressure at different points when the speed is known. It gives a simple way to connect pressure and motion in fluid flow.

Bernoulli’s Equation in Streamlined Flow

characteristics of fluids

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pascal's law

Pascal’s Principle in Static Fluids

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archimedes' principle

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buoyancy

Buoyant Force in Sinking and Floating

Buoyant force explains why objects float, sink, or stay suspended in a fluid. A fluid can be a liquid or a gas, and every object placed in it experiences this upward force. A metal ball sinks, while a rubber ball floats. A submarine also changes its buoyancy to move up or down. The force comes from pressure changes in the fluid. Fluid pressure increases with depth because the weight of the fluid above also increases. That means the bottom of an object feels more pressure than the top. This...

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Wetting and Surface Curvature

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Capillary Action in Thin Tubes

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laminar and turbulent flow

Fluid Motion Patterns in Air and Water

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bernoulli's equation

Fluid Pressure and Speed in Motion

Bernoulli's equation connects fluid pressure with fluid speed. It helps explain why moving fluids can create pressure changes in everyday situations. One example is when two trains pass each other quickly and seem to pull inward. The same effect can happen when two cars pass each other at high speed. As the air between the trains or cars speeds up, its pressure drops. The air on the outside stays at atmospheric pressure. That pressure difference creates a net inward force on the vehicles.

bernoulli's principle

Fluid Pressure and Speed Changes

Bernoulli's equation links fluid pressure and fluid speed in a static, incompressible fluid. For horizontal flow, where gravitational energy density stays constant, the equation is especially useful. In that setting, the result is known as Bernoulli's principle. Bernoulli's principle says that fluid pressure drops when speed increases, and pressure rises when speed decreases. This pressure-speed relationship helps explain how moving fluids behave in simple flow situations. It also provides a...

bernoulli's principle: applications

Bernoulli's Principle in Fluid Devices

Bernoulli's principle helps explain how many fluid devices work when the fluid moves at a constant height. It is useful for devices that use fast flow to create low pressure and for devices that measure fluid speed. Some devices use this pressure change to pull one fluid into another. These are called entrainment devices. A Bunsen burner uses an adjustable gas nozzle to entrain air for proper combustion. An atomizer uses a squeeze bulb to make a jet of air that pulls perfume drops into the...

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energy conservation and bernoulli's equation

Bernoulli’s equation describes energy in a moving fluid. It comes from the conservation of energy principle, or the work-energy theorem, applied to an incompressible, inviscid fluid in laminar, steady, irrotational flow. The equation says that pressure energy, potential energy, and kinetic energy per unit volume stay constant along a streamline. Each term has the units of energy per unit volume. The kinetic energy per unit volume is called kinetic energy density, and the potential energy per...

viscosity

Viscosity and How Fluids Flow

Viscosity describes how easily a fluid flows. Water moves quickly, while honey and maple syrup flow slowly and stick to a surface. That difference comes from fluid friction between liquid layers and between a fluid and the material around it. In this example, water has a lower viscosity than honey and maple syrup. Viscosity is measured in newton-second per meter squared (N·s/m2) or pascal-second (Pa·s). It also changes with temperature and can differ from one fluid to another by several orders...

poiseuille's law and reynolds number

Fluid Resistance, Viscosity, and Flow Regime

Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate. Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size...

stokes' law

Terminal Velocity in a Viscous Fluid

Viscous forces act like friction in a liquid. They resist the relative motion of molecules and pull back on a solid body moving through the fluid. The size of this force depends on the body’s shape and size, its speed, and the liquid’s viscosity, density, and temperature. For a spherical solid object, the force in a fluid is described by Stokes’ law. This law applies only at low Reynolds number, when the flow is laminar and not turbulent. Experiments show that the force is proportional to the...

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key terms and concepts

Learn how Bernoulli’s equation links pressure, speed, and energy in laminar fluid flow, and why incompressible conditions matter.

Bernoulli’s Equation in Streamlined Flow | JoVE K12

physics

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Bernoulli’s Equation in Streamlined Flow

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