Name: laminar flow profile between parallel plates
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 17 s
Channel: JoVE

Il flusso laminare costante tra due piastre parallele descrive il movimento del fluido in un canale stretto e confinato, spesso utilizzato per modellare semplici sistemi di fluidi.
Per il flusso tra due piastre fisse, le equazioni di Navier-Stokes semplificano poiché la velocità varia solo perpendicolarmente alle piastre, senza accelerazione lungo la direzione del flusso.
Ciò porta a un profilo di velocità parabolico, in cui il fluido si muove più velocemente al centro e rallenta a zero alle piastre a causa dell'attrito, noto come condizione di non scivolamento.
La portata tra le piastre dipende dal gradiente di pressione, dalla viscosità del fluido e dalla separazione delle piastre; l'allargamento della fessura o l'aumento del gradiente di pressione migliora il flusso.
La velocità media del flusso è anche correlata alla caduta di pressione, con la velocità di picco al centro del canale che è 1,5 volte la velocità media.
Questa analisi rimane valida solo per bassi numeri di Reynolds, che indicano condizioni laminari, e fallisce per flussi turbolenti ad alto numero di Reynolds.
Le applicazioni di questa analisi includono canali di irrigazione, flusso delle acque sotterranee e bacini di sedimentazione negli impianti di trattamento delle acque, dove esistono condizioni laminari.

flusso laminare stazionario tra piastre parallele

Steady, Laminar Flow Between Parallel Plates

Comprendere il flusso laminare stazionario tra piastre parallele, è essenziale per analizzare e progettare il flusso in stretti canali rettangolari, comunemente presenti in vari sistemi di trasporto e drenaggio dell'acqua. Le equazioni di Navier-Stokes, regolano il moto del fluido e sono generalmente difficili da risolvere a causa della loro non linearità. Tuttavia, in alcuni casi, sono possibili delle semplificazioni, come nel flusso laminare stazionario tra piastre parallele. Per questo scenario, assumiamo un flusso laminare stazionario, incomprimibile.

Considerando due piastre orizzontali, allineate lungo l'asse x e distanziate di una distanza di '2h', l'una dall'altra, con l'asse y perpendicolare alle piastre, si presume che il moto del fluido sia parallelo. Qui, l'equazione di continuità, non indica alcuna variazione di velocità lungo l'asse x e le equazioni di Navier-Stokes, si semplificano come segue:

<img alt="Equation 1" src="/files/ftp_upload/18063/18063_Equation_1.svg" style="text-align: center; height: 30px;">

Le equazioni nelle direzioni y e z, non mostrano un gradiente di pressione lungo questi assi, indicando che la pressione varia in modo idrostatico nella direzione y, consentendo di integrare ed ottenere:

<img alt="Equation 2" src="/files/ftp_upload/18063/18063_Equation_2.svg" style="text-align: center; height: 12px;">

Per piastre parallele, con un gradiente di pressione lungo l'asse x, l'equazione si semplifica come segue:

<img alt="Equation 3" src="/files/ftp_upload/18063/18063_Equation_3.svg" style="text-align: center; height: 30px;">

Integrando due volte e applicando le condizioni al contorno (u = 0 a y = +h e y = -h), si ottiene:

<img alt="Equation 4" src="/files/ftp_upload/18063/18063_Equation_4.svg" style="text-align: center; height: 30px;">

Questa espressione, rivela che il profilo di velocità attraverso lo spazio tra le piastre è parabolico, con velocità massima a y = 0, a metà strada tra le piastre. La portata volumetrica attraverso una larghezza unitaria delle piastre, si ottiene integrando il profilo di velocità attraverso lo spazio.

La comprensione del flusso laminare tra piastre parallele, ha applicazioni pratiche nel flusso delle acque sotterranee, nel trattamento delle acque reflue e nella lubrificazione. Ad esempio, questo modello può approssimare il flusso negli strati del terreno, dove l'acqua si muove tra le particelle del terreno, come il flusso tra le piastre. Conoscere la portata e la distribuzione della velocità, aiuta gli ingegneri a progettare sistemi di drenaggio efficienti e a prevedere il movimento delle acque sotterranee.

Flusso Laminare Stazionario tra Piastre Parallele

Il flusso laminare costante tra due piastre parallele descrive il movimento del fluido in un canale stretto e confinato, spesso utilizzato per modellare semplici sistemi di fluidi.
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JoVE Core

Civil Engineering

Ingegneria Civile

Unit 1

Unità 1

Differential Analysis of Fluid Flow

Analisi differenziale del flusso di fluidi

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

laminar flow profile between parallel plates

Laminar flow between parallel plates shows how fluid moves through a narrow, flat channel. This model helps describe flow in water conveyance and drainage systems, where the space is limited and the motion stays orderly. It is also useful for analyzing flow in rectangular channels used in many engineering settings.

The flow is studied with the Navier-Stokes equations, which govern fluid motion. These equations are often difficult to solve because they are nonlinear. In this case, the problem becomes simpler because the flow is steady, incompressible, and laminar. Two horizontal plates are placed along the x-axis, and the gap between them is 2h. The y-axis is perpendicular to the plates, and the fluid moves parallel to the plates.

With these assumptions, the continuity equation shows that the velocity does not change along the x-axis. The Navier-Stokes equations also simplify in the y and z directions. They show no pressure gradient along those axes, so pressure changes hydrostatically in the y-direction. After integration, the x-direction equation includes the pressure gradient along the plates.

Solving that equation requires integrating twice and applying the no-slip boundary conditions, where u = 0 at y = +h and y = -h. The result is a parabolic velocity profile across the gap. The fluid moves fastest at y = 0, the midpoint between the plates. The volumetric flow rate for a unit width of the plates is then found by integrating the velocity profile across the space.

This flow model has practical uses in groundwater flow, wastewater treatment, and lubrication. It can also represent water moving through soil layers, where the flow resembles movement between plates. Engineers use the velocity distribution and flow rate to help design drainage systems and predict groundwater movement.

Laminar Flow Profile Between Parallel Plates

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steady, laminar flow between parallel plates

Laminar flow between parallel plates shows how fluid moves through a narrow, flat channel. This model helps describe flow in water conveyance and drainage systems, where the space is limited and the motion stays orderly. It is also useful for analyzing flow in rectangular channels used in many engineering settings. The flow is studied with the Navier-Stokes equations, which govern fluid motion. These equations are often difficult to solve because they are nonlinear. In this case, the problem...

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Learn how steady laminar flow between parallel plates leads to a parabolic velocity profile, pressure-gradient behavior, and flow-rate calculations.

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Laminar Flow Profile Between Parallel Plates

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