Name: fluid head profiles in pipes and channels
Uploaded: 2025-02-13T15:43:14.000Z
Duration: 1 min 27 s
Channel: JoVE

In un fluido che scorre attraverso un tubo, la linea di energia rappresenta l'energia totale del fluido, combinando pressione, velocità e carichi di elevazione.
Al contrario, la linea del gradiente idraulico mostra solo la somma dei carichi di pressione e di elevazione, esclusa la velocità.
Queste linee rappresentano visivamente la distribuzione dell'energia e della pressione in un sistema di flusso di fluidi.
La differenza tra queste linee è la testa di velocità; la linea di energia è sempre maggiore della linea di gradiente idraulico durante il flusso.
In un fluido stazionario, le linee di gradiente energetico e idraulico coincidono.
La pressione positiva si verifica quando la linea di gradiente idraulico si trova sopra il tubo; la pressione negativa si verifica quando è al di sotto, causando potenzialmente problemi come la cavitazione.
Il mantenimento del gradiente idraulico al di sopra dell'elevazione del tubo previene problemi come il trascinamento dell'aria e il cedimento strutturale della tubazione.
Nei sistemi a sifone, la comprensione di queste linee garantisce una pressione adeguata per sostenere un flusso ininterrotto.
Il monitoraggio di queste linee aiuta a rilevare perdite o ostruzioni e a progettare sistemi per evitare colpi d'ariete o riflusso.
Strumenti come i tubi di Pitot e i piezometri misurano queste linee, aiutando nella progettazione e nell'analisi dei sistemi idraulici nell'ingegneria civile.

linea energetica e linea di gradiente idraulico

Energy Line and Hydraulic Gradient Line

In base all'equazione di Bernoulli, la linea energetica (EL) e la linea di pendenza idraulica (HGL), forniscono rappresentazioni grafiche della distribuzione di energia in un sistema di flusso di fluidi. Per flussi costanti, incomprimibili e non viscosi, l'equazione di Bernoulli è espressa come:

<img alt="Equation 1" src="/files/ftp_upload/18039/18039_Equation_1.svg" style="text-align: center; height: 34px;">

Qui, H è la prevalenza totale, p/γ​ è la prevalenza di pressione, V^2/2g​ è la prevalenza di velocità e z è la prevalenza di elevazione.

La linea energetica (EL) rappresenta la prevalenza totale disponibile nel flusso. Si trova sopra il dato e include tutte e tre le componenti energetiche. In condizioni ideali, rimane orizzontale, poiché l'energia totale non varia lungo una linea di flusso. L'elevazione della EL può essere misurata utilizzando un tubo di Pitot, che cattura la pressione di ristagno e fornisce il valore di energia totale.

La linea di pendenza idraulica (HGL) raffigura la prevalenza piezometrica (p/γ+ z), che esclude la prevalenza di velocità. Si trova al di sotto dell'EL per una distanza verticale, che è uguale alla prevalenza di velocità (V^2/2g​). L'HGL rappresenta le variazioni di pressione all'interno del sistema. Nelle condotte pressurizzate, si trova al di sopra del tubo, mentre nel flusso a canale aperto, coincide con la superficie dell'acqua.

Se la velocità del fluido o il diametro del tubo cambiano, l'elevazione dell'HGL si regola di conseguenza. La prevalenza di pressione è zero all'uscita del tubo, facendo coincidere l'HGL con la prevalenza di elevazione. Per un flusso costante e non viscoso che fuoriesce da un serbatoio, l'EL e l'HGL sono orizzontali, riflettendo una prevalenza costante e una pressione atmosferica di uscita.

Le applicazioni pratiche spesso incorporano effetti viscosi e perdite, che distorcono l'EL e l'HGL. Questi concetti sono cruciali per analizzare la pressione e le distribuzioni di energia nei sistemi fluidi.

Linea Energetica e Linea di Gradiente Idraulico

In un fluido che scorre attraverso un tubo, la linea di energia rappresenta l'energia totale del fluido, combinando pressione, velocità e carichi di elevazione.
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fluid head profiles in pipes and channels

Fluid head profiles in pipes and channels show how pressure, speed, and height change in a flowing fluid. These profiles come from Bernoulli's equation for steady, incompressible, inviscid flow. In that equation, total head includes pressure head, velocity head, and elevation head.

The energy line (EL) shows the total head available in the flow. It sits above the datum and includes all three energy parts. Under ideal conditions, the EL stays horizontal because the total energy does not change along a streamline. A Pitot tube can be used to measure the EL by capturing stagnation pressure and giving the total energy value.

The hydraulic grade line (HGL) shows the piezometric head, which is the pressure head plus the elevation head. It does not include the velocity head. The HGL lies below the EL by a vertical distance equal to the velocity head, V²/2g. It helps show pressure changes in the system.

In a pressurized pipeline, the HGL is usually above the pipe. In open-channel flow, it matches the water surface. If fluid velocity changes or the pipe diameter changes, the HGL position changes too. At a pipe outlet, pressure head is zero, so the HGL meets the elevation head.

For steady, inviscid flow from a tank, both the EL and HGL are horizontal. This reflects constant head and atmospheric pressure at the outlet. In real systems, viscous effects and losses can bend these lines. These ideas are important for reading pressure and energy in fluid systems.

Fluid Head Profiles in Pipes and Channels

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energy line and hydraulic gradient line

Fluid head profiles in pipes and channels show how pressure, speed, and height change in a flowing fluid. These profiles come from Bernoulli's equation for steady, incompressible, inviscid flow. In that equation, total head includes pressure head, velocity head, and elevation head. The energy line (EL) shows the total head available in the flow. It sits above the datum and includes all three energy parts. Under ideal conditions, the EL stays horizontal because the total energy does not change...

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Water slide speed is controlled by Bernoulli's principle and the height of the slide. Engineers use these ideas to keep the ride exciting while making sure the water stays safe for riders. As water moves downhill, gravity makes it speed up. The water at the bottom depends on the height it starts from. A taller slide gives the water more potential energy at the top. That energy changes into kinetic energy as the water descends, so the flow becomes faster. Bernoulli's principle helps describe...

key terms and concepts

Learn how the energy line and hydraulic grade line show total head, pressure changes, and velocity effects in pipes, tanks, and open channels.

Fluid Head Profiles in Pipes and Channels | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Fluid Head Profiles in Pipes and Channels

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