Name: water slide speed and bernoulli's principle
Uploaded: 2025-02-13T15:43:15.000Z
Duration: 1 min 18 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Specialised Topic in Science

112.51.c.1.

112.51.c.2.D.

Design Example: Designing Water Slide

Un ingénieur conçoit un toboggan aquatique pour un parc aquatique, où l’eau s’écoule pour créer un manège rapide et sûr pour les visiteurs du parc.
Le toboggan mesure 25 mètres de long et commence à une hauteur de 10 mètres, avec une vitesse de sécurité de 12 mètres par seconde en bas.
L'équation de Bernoulli aide à calculer la vitesse de l'eau, en reliant l'énergie potentielle, l'énergie cinétique et la pression aux deux points qui sont ouverts à l'air. Il ne suppose aucun frottement et traite l’eau comme un fluide idéal.
Au sommet du toboggan, l’eau est au repos et sa vitesse augmente au fur et à mesure qu’elle descend.
Avec la hauteur du toboggan de 10 mètres, la vitesse calculée de l'eau au fond est d'environ 14 mètres par seconde, ce qui dépasse la limite de sécurité.
La hauteur du toboggan doit être abaissée pour réduire la vitesse à un niveau sûr.
Après avoir recalculé pour une vitesse de 12 mètres par seconde, la hauteur du toboggan doit être réduite à environ 7,34 mètres.
Cela garantit que l’eau s’écoule en toute sécurité sur le toboggan, l’empêchant de dépasser la vitesse de sécurité lorsqu’elle atteint le fond.

exemple de conception: conception d'un toboggan aquatique

Lors de la conception d'un toboggan aquatique, le contrôle de la vitesse d'écoulement de l'eau est essentiel pour la sécurité des utilisateurs tout en préservant l'expérience. Lorsque l'eau descend le long du toboggan, la gravité l'accélère, sa vitesse en bas dépendant de la hauteur à laquelle elle démarre. Plus le toboggan est haut, plus l'eau a d'énergie potentielle en haut, qui est convertie en énergie cinétique lors de sa descente, augmentant ainsi sa vitesse.

Le principe de Bernoulli détermine la vitesse de l'eau le long du toboggan. Le principe relie l'énergie potentielle au point 1, le haut, l'énergie cinétique au point 2, le bas, et la pression de l'eau aux deux points.

<img alt="Equation 1" src="/files/ftp_upload/18040/18040_Equation_1.svg" style="text-align: center; height: 28px;">

Dans un toboggan aquatique, lorsque l'eau descend, son énergie potentielle diminue tandis que son énergie cinétique augmente, ce qui entraîne une augmentation de la vitesse. L'équation de Bernoulli suppose l'absence de frottement et traite l'eau comme un fluide idéal, ce qui signifie qu'elle s'écoule sans perte d'énergie due au frottement ou à la turbulence. Ces hypothèses simplifient les calculs, même si dans des scénarios réels, la friction peut légèrement réduire la vitesse réelle de l'eau.

Au sommet du toboggan, l'eau est presque au repos et, au fur et à mesure de sa descente, elle accélère. Si le toboggan est trop haut, l'eau peut atteindre des vitesses dangereuses en bas, ce qui présente des risques pour les utilisateurs. Par conséquent, il est nécessaire d'ajuster la hauteur h du toboggan pour maintenir la vitesse de l'eau dans des limites sûres. En calculant la hauteur appropriée à l'aide du principe de Bernoulli, le toboggan peut réduire la vitesse de l'eau tout en offrant une expérience palpitante.

<img alt="Equation 2" src="/files/ftp_upload/18040/18040_Equation_2.svg" style="text-align: center; height: 36px;">

Exemple de conception: conception d'un toboggan aquatique

Un ingénieur conçoit un toboggan aquatique pour un parc aquatique, où l’eau s’écoule pour créer un manège rapide et sûr pour les visiteurs du parc.
Le toboggan fait 25 mètres ...

Education

Enseignement

JoVE Core

Civil Engineering

Génie civil

Unit 1

Unité 1

Fluid Dynamics

Dynamique des fluides

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

water slide speed and bernoulli's principle

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 the water's velocity along the slide. It connects the potential energy at point 1, near the top, with the kinetic energy at point 2, near the bottom, as well as the pressure of the water at both points. As the water moves down the slide, its potential energy decreases and its kinetic energy increases. This leads to a higher velocity near the bottom.

The calculation uses an ideal fluid model. That means the water is treated as if it flows without friction or turbulence, so no energy is lost in the equation. Real water can have some friction, so the actual speed may be a little lower. At the top of the slide, the water is nearly at rest. If the slide is too tall, the water can reach unsafe speeds at the bottom. That is why the height h must be adjusted to keep the velocity within safe limits while still giving riders a thrilling ride.

Water Slide Speed and Bernoulli's Principle

water-slide-speed-and-bernoullis-principle

bernoulli's equation for flow along a streamline

bernoulli-s-equation-for-flow-along-a-streamline

Pressure and Speed in Bernoulli's Equation

Bernoulli's equation links pressure, speed, and height in a moving fluid along a streamline. It is used for incompressible, inviscid fluids under steady flow. The idea comes from applying Newton's second law to a small fluid element. That element feels forces from pressure differences, gravity, and changes in velocity. The resulting equation shows how fluid energy is shared. In the equation, P is pressure, ρ is fluid density, v is velocity, g is the acceleration due to gravity, and h is...

bernoulli's equation for flow normal to a streamline

bernoulli-s-equation-for-flow-normal-to-a-streamline

Pressure Changes Across Curved Streamlines

Bernoulli's equation for flow normal to a streamline describes how pressure changes across curved streamlines. When a fluid follows a curved path, the outer side of the curve experiences centrifugal force, which pushes the fluid outward. The pressure is therefore higher on the inner side, near the center of curvature, and lower farther out. The size of this pressure difference depends on the fluid's velocity and the radius of curvature. In flows with nearly straight streamlines, the pressure...

bernoulli's equation: problem solving

Venturi Meter Flow Rate from Pressure

A Venturi meter measures fluid flow rate in a pipeline by using pressure changes and Bernoulli's equation. In a sewage system, it can be used to determine wastewater flow rate by reading the pressure difference across the meter. The narrowed throat makes the fluid speed up, and that change in speed is linked to pressure drop. The first step is to find the cross-sectional areas of the pipe and the Venturi throat. These areas are needed to interpret the pressure difference shown on the pressure...

static, stagnation, dynamic and total pressure

static-stagnation-dynamic-and-total-pressure

Pitot-Static Measurement in Bernoulli Flow

Static pressure, dynamic pressure, stagnation pressure, and total pressure are key ideas in fluid dynamics. They are often explained with Bernoulli's equation. In that equation, p is static pressure, 1/2ρV^2 is dynamic pressure, γz is hydrostatic pressure or potential energy pressure, and pT is total pressure. For incompressible flow, the total pressure stays constant along a streamline. Static pressure is the pressure a fluid exerts when it is at rest, or when flowing fluid is brought to rest...

free jet

Liquid Speed from Reservoir Outlets

Free jets show how liquid moves after leaving a reservoir through an opening and flowing into the air without resistance. The jet speed is found with Bernoulli’s principle, and it depends on the height of liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit. The liquid column’s height controls the speed at the nozzle because the fluid’s potential energy changes into kinetic energy during flow. As the liquid leaves the...

continuity equation

Fluid Flow and Area Changes

Fluid flow and area changes are linked by the continuity equation. For a steady flow of an incompressible fluid in a confined system, the mass flow rate stays constant. This idea is useful in nozzles, syringes, and pipes where the cross-sectional area changes. The mass flow rate is written as an equation that connects density, area, and velocity. For incompressible flow, the density stays the same, so the equation becomes simpler. When the area gets smaller, the fluid speed must increase. When...

energy line and hydraulic gradient line

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...

design example: designing water slide

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 Bernoulli's principle and slide height control water speed on a waterslide. See how potential energy becomes kinetic energy and affects rider safety.

Water Slide Speed and Bernoulli's Principle | 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

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Ask questions and define problems related to specialized topics of study based on observations or information from text, phenomena, models, or investigations;

112.51.c.1.A.

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112.51.c.1.B.

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112.51.c.1.C.

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112.51.c.1.D.

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Collect quantitative data using the International System of Units (SI) or qualitative data as evidence as appropriate to the specialized topic of study;

112.51.c.1.E.

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112.51.c.1.F.

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112.51.c.1.H.

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112.51.c.2.A.

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112.51.c.2.C.

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Water Slide Speed and Bernoulli's Principle

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