Name: pressure and velocity in inviscid flow
Uploaded: 2025-02-13T15:43:25.000Z
Duration: 1 min 28 s
Channel: JoVE

In un fluido in movimento, le sollecitazioni di taglio si sviluppano a causa della viscosità. Per l'acqua, che ha una bassa viscosità, questi effetti sono trascurabili, semplificando l'analisi del movimento dei fluidi.
Quando le sollecitazioni di taglio sono trascurabili, il fluido è considerato invisibile o privo di attrito. Nei fluidi invisibili, la sollecitazione normale è la stessa in tutte le direzioni, il che significa che la pressione è indipendente dalla direzione della sollecitazione.
La pressione è il negativo della sollecitazione normale, garantendo che le sollecitazioni di compressione si traducano in un valore di pressione positivo.
Le equazioni generali del moto per il flusso inviscido, note come equazioni di Eulero, descrivono la conservazione della quantità di moto. Queste equazioni rappresentano la seconda legge di Newton applicata a un elemento fluido, che mette in relazione le variazioni di velocità con le forze che agiscono sul fluido.
Le equazioni di Eulero tengono conto dei gradienti di pressione, delle forze corporee come la gravità e delle accelerazioni, sia locali che convettive, che guidano i cambiamenti nella velocità del fluido.
Trascurano le forze viscose, semplificando l'analisi, ma rimangono difficili da risolvere a causa dei termini di velocità non lineari nelle equazioni differenziali alle derivate parziali.
L'integrazione delle equazioni di Eulero lungo una linea di linee guida deriva l'equazione di Bernoulli, fornendo informazioni sulle variazioni di pressione, velocità ed elevazione nei flussi inviscidi, rendendola uno strumento chiave nella meccanica dei fluidi.

equazioni del moto di eulero

Euler&#39;s Equations of Motion

Nella meccanica dei fluidi, gli sforzi di taglio derivano dalla viscosità, che rappresenta la resistenza interna di un fluido alla deformazione. Per i fluidi a bassa viscosità, come l'acqua, questi sforzi sono minimi, semplificando l'analisi del flusso e consentendo di trattare il fluido come non viscoso, o privo di attrito. In un fluido non viscoso, gli sforzi di taglio sono assenti, sono presenti solo gli sforzi normali, che agiscono perpendicolarmente agli elementi del fluido. In particolare, la pressione, definita come il negativo dello sforzo normale, rimane uniforme in diverse direzioni e non è influenzata dall'orientamento dello sforzo.

Il moto dei fluidi non viscosi, è governato dalle equazioni di Eulero, derivate dalla seconda legge di Newton applicata alla dinamica dei fluidi. Queste equazioni descrivono la conservazione della quantità di moto, correlando la velocità di variazione della velocità, alle forze che agiscono su un elemento fluido. Per un fluido non viscoso, le forze rilevanti includono gradienti di pressione e forze del corpo, come la gravità. Le equazioni di Eulero esprimono l'equilibrio di queste forze, escludendo i termini viscosi:

<img alt="Equation 1" src="/files/ftp_upload/18057/18057_Equation_1.svg" style="text-align: center; height: 30px;">

dove ρ è la densità del fluido, v è il vettore velocità, p è la pressione e g​ rappresenta l'accelerazione gravitazionale.

Pur trascurando la viscosità, le equazioni di Eulero rimangono complesse a causa dei loro termini non lineari, che tengono conto dell'accelerazione convettiva delle particelle di fluido. Quando integrate lungo una linea di flusso, queste equazioni producono l'equazione di Bernoulli, che descrive una relazione fondamentale nella meccanica dei fluidi, collegando pressione, velocità ed elevazione per flussi non viscosi. L'equazione di Bernoulli è un potente strumento per analizzare la distribuzione di energia all'interno dei flussi di fluidi, supportando applicazioni nel trasporto di fluidi, aerodinamica e idrodinamica.

Equazioni del Moto di Eulero

In un fluido in movimento, le sollecitazioni di taglio si sviluppano a causa della viscosità. Per l'acqua, che ha una bassa viscosità, questi effetti sono trascurabili, semplificando il movimento del fluido ...

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Differential Analysis of Fluid Flow

Analisi differenziale del flusso di fluidi

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

pressure and velocity in inviscid flow

Pressure and velocity in inviscid flow are linked by Euler's equations of motion. In fluid mechanics, viscosity creates shear stress, which is a force that acts along a surface. For low-viscosity fluids like water, these shear stresses are very small. That lets the fluid be treated as inviscid, or frictionless.

In an inviscid fluid, shear stresses are absent. Only normal stresses remain, and these act perpendicular to a fluid element. Pressure is the negative of the normal stress. It stays the same in different directions and does not depend on how the stress is oriented.

Euler's equations come from Newton's second law applied to fluid motion. They describe momentum conservation by linking the change in velocity to the forces on a fluid element. For inviscid flow, those forces are pressure gradients and body forces such as gravity. The equations include density, velocity, pressure, and gravitational acceleration, but they leave out viscous terms.

Even without viscosity, Euler's equations are still nonlinear. That means they are complex because they include convective acceleration, which follows the motion of fluid particles. When the equations are integrated along a streamline, they lead to Bernoulli's equation. Bernoulli's equation connects pressure, velocity, and elevation in inviscid flows and is useful for fluid transport, aerodynamics, and hydrodynamics.

Pressure and Velocity in Inviscid Flow

euler&#39;s equations of motion

Pressure and velocity in inviscid flow are linked by Euler's equations of motion. In fluid mechanics, viscosity creates shear stress, which is a force that acts along a surface. For low-viscosity fluids like water, these shear stresses are very small. That lets the fluid be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent. Only normal stresses remain, and these act perpendicular to a fluid element. Pressure is the negative of the normal stress. It stays the...

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navier&#8211;stokes equations

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key terms and concepts

Learn how pressure, velocity, and gravity shape inviscid fluid motion through Euler's equations, and how they lead to Bernoulli's equation along a streamline.

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civil engineering

Pressure and Velocity in Inviscid Flow

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