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

Załóżmy, że nieściśliwy, laminarny płyn w stanie ustalonym przechodzi przez rurkę o niejednorodnym przekroju poprzecznym.
Ponieważ płyn jest nieściśliwy, objętość pierwiastka płynu i jego masa pozostają stałe.
Prędkość elementu płynnego wchodzącego i wychodzącego z rurki jest różna, co powoduje zmianę energii kinetycznej netto.
Siła działająca na element płynu wynika z ciśnienia otoczenia płynu.
Tak więc praca netto wykonana na elemencie płynu przez otaczający płyn podczas przemieszczenia jest różnicą między pracą wykonaną podczas wchodzenia i wychodzenia z rury.
Kiedy płynny pierwiastek przechodzi przez wyniesiony obszar, zyskuje grawitacyjną energię potencjalną i określa się zmianę grawitacyjnej energii potencjalnej.
Zgodnie z twierdzeniem o energii kinetycznej pracy, praca netto wykonana na elemencie płynnym jest równa zmianie energii kinetycznej.
Dzieląc przez wspólną wartość, otrzymuje się równanie.
Wzdłuż linii strumienia całkowita energia na jednostkę objętości przepływającego płynu jest stała, nazywana równaniem Bernoulliego.

<ol>
	<li>Young, H.D i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson: sekcja 12.5; strony 385–386.</li>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 1. [Wersja internetowa]. Pobrane z <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>: sekcja 14.6; strony 716–718.</li>
</ol>

zasada zachowania energii i równanie bernoulliego

Zastosowanie zasady zachowania energii lub twierdzenia o energii pracy do nieściśliwego, nielepkiego płynu w laminarnym, ustalonym, bezwirowym przepływie prowadzi do równania Bernoulliego. Stwierdza, że suma ciśnienia płynu, potencjału i energii kinetycznej na jednostkę objętości jest stała wzdłuż linii prądu.

Wszystkie wyrazy w równaniu mają wymiar energii na jednostkę objętości. Energia kinetyczna na jednostkę objętości nazywana jest gęstością energii kinetycznej, a energia potencjalna na jednostkę objętości nazywana jest gęstością energii potencjalnej.

Należy pamiętać, że gęstość cieczy nie powinna zmieniać się w trakcie przepływu; to znaczy powinien być nieściśliwy. Przepływ powinien być również laminarny i nie turbulentny. Równanie Bernoulliego ma zastosowanie do gazów, które mają znikomy wpływ na ściśliwość. Dla takich gazów przyjmuje się, że gęstość jest stała i traktuje się je jak płyn nieściśliwy. Ponieważ gazy są ogólnie ściśliwe, równanie nie ma do nich zastosowania.

Chociaż jest to proste powtórzenie zasady zachowania energii z kilkoma krytycznymi założeniami, równanie ułatwia obliczenie ciśnienia w różnych punktach, jeśli znane są prędkości.

Zasada zachowania energii i równanie Bernoulliego

Zastosowanie zasady zachowania energii lub twierdzenia o energii pracy do nieściśliwego, nielepkiego płynu w laminarnym, stałym, irrotacyjnym przepływie prowadzi ...

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energy-conservation-and-bernoulli-s-equation

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Fluid Mechanics

Mechanika płynów

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

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rise of liquid in a capillary tube

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bernoulli's principle

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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

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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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