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

Um engenheiro está projetando um toboágua para um parque aquático, onde a água flui para criar um passeio rápido e seguro para os visitantes do parque.
O escorregador tem 25 metros de comprimento e começa a uma altura de 10 metros, com uma velocidade segura de 12 metros por segundo na parte inferior.
A equação de Bernoulli ajuda a calcular a velocidade da água, relacionando a energia potencial, a energia cinética e a pressão em ambos os pontos que estão abertos ao ar. Não pressupõe atrito e trata a água como um fluido ideal.
No topo do escorregador, a água está em repouso e sua velocidade aumenta à medida que desce.
Com a altura do escorregador de 10 metros, a velocidade calculada da água no fundo é de aproximadamente 14 metros por segundo, o que excede o limite seguro.
A altura do escorregador deve ser reduzida para reduzir a velocidade a um nível seguro.
Após recalcular para uma velocidade de 12 metros por segundo, a altura do slide deve ser reduzida para aproximadamente 7,34 metros.
Isso garante que a água flua pelo escorregador com segurança, evitando que exceda a velocidade segura ao atingir o fundo.

exemplo de design: projetando um toboágua

Ao projetar um toboágua, controlar a velocidade do fluxo de água é crucial para a segurança do usuário, mantendo uma experiência emocionante. Conforme a água desce pelo toboágua, a gravidade faz com que ela acelere, com sua velocidade na parte inferior dependendo da altura de onde começa. Quanto mais alto o toboágua, mais energia potencial a água tem no topo, convertida em energia cinética à medida que desce, aumentando sua velocidade.

O princípio de Bernoulli determina a velocidade da água ao longo do toboágua. O princípio relaciona a energia potencial no ponto 1, o topo, a energia cinética no ponto 2, o fundo, e a pressão da água em ambos os pontos.

<img alt="Equation 1" src="/files/ftp_upload/18040/18040_Equation_1.svg" style="text-align: center; height: 28px;">

Em um toboágua, conforme a água desce, sua energia potencial diminui enquanto sua energia cinética aumenta, levando a um aumento na velocidade. A equação de Bernoulli não assume atrito e trata a água como um fluido ideal, o que significa que ela flui sem perda de energia devido ao atrito ou turbulência. Essas suposições simplificam os cálculos, embora em cenários do mundo real, o atrito possa reduzir ligeiramente a velocidade real da água.

No topo do tobogã, a água está quase em repouso e, à medida que desce, acelera. Se o tobogã for muito alto, a água pode atingir velocidades perigosas na parte inferior, representando riscos para os passageiros. Portanto, ajustar a altura h do tobogã é necessário para manter a velocidade da água em limites seguros. Ao calcular a altura apropriada usando o princípio de Bernoulli, o tobogã pode reduzir a velocidade da água ao mesmo tempo, em que oferece um passeio emocionante.

<img alt="Equation 2" src="/files/ftp_upload/18040/18040_Equation_2.svg" style="text-align: center; height: 36px;">

Exemplo de design: projetando um toboágua

Um engenheiro está projetando um toboágua para um parque aquático, onde a água flui para criar um passeio rápido e seguro para os visitantes do parque.
O escorregador tem 25 metros ...

Education

JoVE Core

Civil Engineering

Engenharia Civil

Unit 1

Unidade 1

Fluid Dynamics

Dinâmica de Fluidos

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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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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.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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Water Slide Speed and Bernoulli's Principle

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