Name: fluid flow in narrowing pipes
Uploaded: 2023-04-30T11:05:06.000Z
Duration: 1 min 12 s
Channel: JoVE

The volume of fluid flowing through a point in an area in unit time gives the volume flow rate.
On substituting volume with area times distance, and using the relation between velocity and distance, volume flow rate equals area times velocity of the fluid.
Consider an incompressible fluid with the same density at all points flowing steadily through an irregular cross-sectional pipe. For a steady flow, the velocity and density of the fluid at a point remain constant with time.
The mass of the fluid passing through a point per unit time is termed as mass flow rate, and it equals density times the volume flow rate.
Since the pipe does not have any other source or sink, the mass flowing into the pipe must equal the mass leaving the pipe. This gives the general equation of continuity for fluids.
For incompressible fluids, density cancels out. Hence, the volume flow rate into the pipe equals the volume flow rate out of the pipe.

vergelijking van continuïteit

Vloeiende beweging wordt weergegeven door snelheidsvectoren of stroomlijnen. Het volume van een vloeistof die gedurende een bepaalde periode langs een bepaalde locatie door een gebied stroomt, wordt de stroomsnelheid Q genoemd, of preciezer gezegd de volumestroomsnelheid. Stroomsnelheid en snelheid zijn gerelateerd: een rivier heeft bijvoorbeeld een grotere stroomsnelheid als de snelheid van het water erin groter is. Het debiet is echter ook afhankelijk van de grootte en vorm van de rivier. De relatie tussen de stroomsnelheid (Q) en de gemiddelde snelheid (v) suggereert dat de stroomsnelheid recht evenredig is met zowel de gemiddelde snelheid van de vloeistof als het dwarsdoorsnedeoppervlak van een rivier, pijp of ander kanaal. Hoe groter de leiding, des te groter is het dwarsdoorsnedeoppervlak. Beschouw een onsamendrukbare vloeistof die door een pijp met afnemende straal stroomt. Omdat de vloeistof hier niet samendrukbaar is, moet dezelfde hoeveelheid vloeistof binnen een bepaalde tijd langs elk punt in de buis stromen om de continuïteit van de stroming te garanderen. De stroom is continu omdat er geen bronnen of putten zijn die massa toevoegen of verwijderen, dus de massa die de buis instroomt moet gelijk zijn aan de massa die uit de buis stroomt. In dit geval is het, omdat het dwarsdoorsnedeoppervlak van de pijp afneemt, noodzakelijk dat de snelheid toeneemt. Deze logica kan worden uitgebreid door te zeggen dat het debiet op alle punten langs de leiding hetzelfde moet zijn. Dit wordt de continuïteitsvergelijking genoemd en geldt voor elke onsamendrukbare vloeistof (met constante dichtheid). Omdat vloeistoffen in wezen onsamendrukbaar zijn, geldt de continuïteitsvergelijking voor alle vloeistoffen. Gassen zijn echter samendrukbaar, dus de vergelijking moet met voorzichtigheid worden toegepast op gassen als deze worden onderworpen aan compressie of expansie. Deze tekst is een bewerking van <a href="https://openstax.org/books/university-physics-volume-1/pages/14-5-fluid-dynamics">Openstax, University Physics Deel 1, Sectie 14.5: Fluid Dynamics. </a>

Vergelijking van continuïteit

Fluid motion is represented by either velocity vectors or streamlines. The volume of a fluid flowing past a given location through an area during a period ...

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Fluid Mechanics

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KEY TERMS AND CONCEPTS

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Equation of Continuity

fluid flow in narrowing pipes

Fluid flow in a pipe is described by flow rate and average speed. Flow rate, or volume flow rate, is the amount of fluid that passes a point through an area in a given time. It depends on both how fast the fluid moves and the size and shape of the conduit.

For a river or pipe, a greater speed usually means a greater flow rate. A larger cross-sectional area also increases flow rate. That is why the same fluid can move differently through conduits of different sizes.

The relationship becomes clear for an incompressible fluid moving through a pipe with a decreasing radius. Because the fluid is incompressible, the same amount of fluid must pass each point in the tube during the same time. This keeps the flow continuous, since no sources or sinks add or remove mass.

As the pipe gets narrower, the cross-sectional area decreases. To keep the flow rate the same, the fluid must move faster. This idea leads to the equation of continuity, which says the flow rate is the same at all points along the pipe.

The equation of continuity applies to any incompressible fluid with constant density. Since liquids are essentially incompressible, the rule works for liquids. Gases can be compressible, so this equation must be used with caution when gases are compressed or expanded.

Fluid Flow in Narrowing Pipes

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equation of continuity

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bernoulli's equation

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bernoulli's principle

Fluid Pressure and Speed Changes

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energy conservation and bernoulli's equation

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Bernoulli’s Equation in Streamlined Flow

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viscosity

Viscosity and How Fluids Flow

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stokes' law

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key terms and concepts

Learn how flow rate, area, and speed stay linked in pipes. See why fluid speeds up in narrow sections and how continuity applies to liquids and gases.

Fluid Flow in Narrowing Pipes | JoVE K12

physics

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Fluid Flow in Narrowing Pipes

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