Name: fluid resistance, viscosity, and flow regime
Uploaded: 2025-05-22T09:05:41.000Z
Duration: 1 min 10 s
Channel: JoVE

In un flusso laminare, attraverso un tubo orizzontale, la portata è definita come il rapporto tra la differenza di pressione in due punti e la resistenza al flusso.
Qui, la resistenza è direttamente proporzionale al coefficiente di viscosità e alla lunghezza del tubo, e inversamente proporzionale alla quarta potenza del raggio del tubo. Se combinata con l'equazione della velocità di flusso, questa relazione fornisce la legge di Poiseuille per il flusso laminare.
Considerando che la viscosità è costante, una leggera diminuzione del raggio del tubo provoca una notevole riduzione della portata. Per mantenere la stessa portata, la differenza di pressione deve aumentare di conseguenza.
Allo stesso modo, è difficile che un fluido più viscoso scorra attraverso il tubo rispetto a un fluido meno viscoso a temperatura costante.
Il numero di Reynolds è un valore che indica se il flusso di un fluido è laminare o turbolento.
Se il numero di Reynolds è inferiore a duemila, il flusso è laminare e turbolento se è maggiore di tremila. Tra i due e i tremila, il flusso è instabile e può mostrare un comportamento caotico.

legge di poiseuille e numero di reynolds

Poiseuille's Law and Reynolds Number

Qualsiasi fluido in un tubo orizzontale può fluire grazie alla differenza di pressione – il fluido fluisce dall'alta alla bassa pressione. La portata (Q) è il rapporto della differenza di pressione e della resistenza attraverso un tubo orizzontale. Maggiore è la differenza di pressione, più alta è la portata. La resistenza del flusso è espressa come:

<img alt="Equation1" src="/files/ftp_upload/12743/12743_Equation_1.png" style="text-align: center; height: 32px;" />

Quando è combinata con la portata (Q), questa relazione fornisce la legge di Poiseuille per il flusso laminare di un fluido incomprimibile in un tubo.

<img alt="Equation2" src="/files/ftp_upload/12743/12743_Equation_2.png" style="text-align: center; height: 32px;" />

Tutti i fattori che riguardano la portata, eccetto la pressione, sono inclusi nella resistenza. La resistenza dipende dalle dimensioni del tubo e dalla viscosità del fluido. La resistenza è direttamente proporzionale alla lunghezza del tubo e inversamente proporzionale alla quarta potenza del raggio del tubo.

Nel caso di un fluido non viscoso, il fluido fluisce senza attrito, e la resistenza al flusso è zero. Questo comporta il movimento di tutti gli strati con la stessa velocità. Al contrario, la resistenza al flusso del fluido nei fluidi viscosi non è zero. In questi casi, la velocità è maggiore al centro della corrente e diminuisce verso il bordo del tubo. Possiamo vedere l'effetto nella fiamma di un bruciatore di Bunsen.

Il flusso può essere considerato laminare o turbolento e classificato secondo il numero di Reynolds. Se il numero di Reynolds è minore di 2,000 il flusso è laminare; se è maggiore di 3,000, il flusso è turbolento. Il flusso è considerato instabile e può mostrare un comportamento caotico se il numero di Reynolds è tra 2,000 e 3,000. Il flusso instabile indica che esso è inizialmente laminare, ma a causa delle ostruzioni o della superficie ruvida, il flusso può diventare turbolento, e potrebbe oscillare casualmente tra l'essere laminare e turbolento. Qui, una piccola variazione in un fattore può avere un effetto esagerato (o non lineare) su un sistema, e quindi mostrare un comportamento caotico.

Questo testo è adattato da <a href="https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence">Openstax, University Physics Volume 1, Section 14.7: Viscosity and Turbulence.</a>

Legge di Poiseuille e numero di Reynolds

Qualsiasi fluido in un tubo orizzontale può fluire a causa delle differenze di pressione: il fluido scorre da alta a bassa pressione. La portata (Q) è il rapporto tra ...

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fluid resistance, viscosity, and flow regime

Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate.

Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size and the fluid's viscosity. It is directly proportional to tube length and inversely proportional to the fourth power of the tube radius.

A non-viscous fluid has frictionless flow, so its resistance is zero. In that case, all layers move at the same speed. Viscous fluids behave differently. Their flow resistance is not zero, and the speed is highest in the middle of the tube and lower near the edges. A Bunsen burner flame can show this effect.

Flow can also be classified by the Reynolds number. When the Reynolds number is below 2,000, the flow is laminar. When it is above 3,000, the flow is turbulent. If the Reynolds number is between 2,000 and 3,000, the flow is unstable and may switch between laminar and turbulent behavior. Small obstructions or surface roughness can trigger this change and lead to chaotic motion.

Fluid Resistance, Viscosity, and Flow Regime

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characteristics of fluids

Fluid Behavior Under Force

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viscosity

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poiseuille's law and reynolds number

Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate. Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size...

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key terms and concepts

Explore how pressure, viscosity, and tube size affect fluid flow. Learn Poiseuille's law, laminar flow, and Reynolds number thresholds in tubes.

Fluid Resistance, Viscosity, and Flow Regime | JoVE K12

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Fluid Resistance, Viscosity, and Flow Regime

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