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

Nehmen wir an, dass eine inkompressible, laminare Flüssigkeit in einem stationären Zustand durch ein Rohr mit ungleichmäßigem Querschnitt strömt.
Da das Fluid inkompressibel ist, bleiben das Volumen des Fluidelements und seine Masse konstant.
Die Geschwindigkeit, mit der das Fluidelement in das Rohr ein- und austritt, ist unterschiedlich, was zu einer Änderung der kinetischen Nettoenergie führt.
Die Kraft, die auf das Fluidelement wirkt, ist auf den Umgebungsdruck des Fluids zurückzuführen.
Die Netzarbeit, die die umgebende Flüssigkeit während der Verdrängung auf das Fluidelement ausübt, ist also die Differenz zwischen der Arbeit, die beim Eintritt in das Rohr und beim Verlassen des Rohrs geleistet wird.
Wenn sich das Fluidelement im erhöhten Bereich bewegt, gewinnt es potentielle Gravitationsenergie und die Änderung der potentiellen Gravitationsenergie wird bestimmt.
Nach dem Satz der arbeitskinetischen Energie entspricht die am Fluidelement geleistete Arbeit der Änderung der kinetischen Energie.
Dividiert man durch einen gemeinsamen Wert, erhält man eine Gleichung.
Entlang einer Stromlinie ist die Gesamtenergie pro Volumeneinheit eines fließenden Fluids eine Konstante, die als Bernoulli-Gleichung bezeichnet wird.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson: Abschnitt 12.5; Seiten 385–386.</li>
	<li>OpenStax. (2019). Universitätsphysik Vol. 1. [Webversion]. Abgerufen von <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>: Abschnitt 14.6; Seiten 716–718.</li>
</ol>

energieeinsparung und bernoullis gleichung

Die Anwendung des Energieerhaltungssatzes oder des Arbeits-Energie-Theorems auf eine inkompressible, nichtviskose Flüssigkeit in laminarer, stationärer, wirbelfreier Strömung führt zur Bernoullis Gleichung. Sie besagt, dass die Summe aus Fluiddruck, Potenzial und kinetischer Energie pro Volumeneinheit entlang einer Stromlinie konstant ist.

Alle Terme in der Gleichung haben die Dimension der Energie pro Volumeneinheit. Die kinetische Energie pro Volumeneinheit wird als kinetische Energiedichte bezeichnet und die potenzielle Energie pro Volumeneinheit als potenzielle Energiedichte.

Es ist wichtig zu beachten, dass die Dichte der Flüssigkeit während der Strömung nicht ändernkonstant bleiben sollte; sie sollte alsosollte, was bedeutet, dass die inkompressibel seinsollte. Die Strömung sollte auch laminar und nicht turbulent sein. Bernoullis Gleichung gilt für Gase, die vernachlässigbare Kompressibilitätseffekte aufweisen. Für solche Gase wird die Dichte als konstant angenommen und als inkompressible Flüssigkeit behandelt. Da Gase generell komprimierbar sind, gilt die Gleichung nicht für sie.

Obwohl es sich um eine einfache Umformulierung des Energieerhaltungsprinzips mit einigen kritischen Annahmen handelt, erleichtert die Gleichung die Berechnung des Drucks an verschiedenen Punkten, wenn die Geschwindigkeiten bekannt sind.

Energieeinsparung und Bernoullis Gleichung

Die Anwendung des Energieerhaltungsprinzips oder des Arbeitsenergiesatzes auf ein inkompressibles, viskoses Fluid in laminarer, stationärer, irrotierender Strömung führt zu ...

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energy-conservation-and-bernoulli-s-equation

Education

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Physics

Physik

Unit 1

Einheit 1

Fluid Mechanics

Strömungsmechanik

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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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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.

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Fluid Pressure and Speed Changes

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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...

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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

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Bernoulli’s Equation in Streamlined Flow

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