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

Ein Ingenieur entwirft eine Wasserrutsche für einen Wasserpark, auf der Wasser nach unten fließt, um den Parkbesuchern eine schnelle und dennoch sichere Fahrt zu ermöglichen.
Die Rutsche ist 25 Meter lang und beginnt in einer Höhe von 10 Metern, mit einer sicheren Geschwindigkeit von 12 Metern pro Sekunde am unteren Rand.
Die Bernoulli-Gleichung hilft bei der Berechnung der Wassergeschwindigkeit, indem sie die potentielle Energie, die kinetische Energie und den Druck an beiden Punkten, die für die Luft offen sind, in Beziehung setzt. Es geht von keiner Reibung aus und behandelt Wasser als ideales Fluid.
Am oberen Ende der Rutsche ruht das Wasser und seine Geschwindigkeit nimmt zu, wenn es absinkt.
Bei einer Höhe der Rutsche von 10 Metern beträgt die berechnete Geschwindigkeit des Wassers am Boden etwa 14 Meter pro Sekunde und überschreitet damit die sichere Grenze.
Die Höhe der Rutsche muss abgesenkt werden, um die Geschwindigkeit auf ein sicheres Niveau zu reduzieren.
Nach einer Neuberechnung für eine Geschwindigkeit von 12 Metern pro Sekunde sollte die Rutschenhöhe auf ca. 7,34 Meter reduziert werden.
Dadurch wird sichergestellt, dass das Wasser sicher die Rutsche hinunterfließt und verhindert, dass es die sichere Geschwindigkeit überschreitet, wenn es den Boden erreicht.

designbeispiel: design einer wasserrutsche

Beim Entwurf einer Wasserrutsche ist die Kontrolle der Fließgeschwindigkeit des Wassers entscheidend für die Sicherheit der Benutzer und gleichzeitig für ein aufregendes Erlebnis. Wenn das Wasser die Rutsche hinunterfließt, beschleunigt es sich aufgrund der Schwerkraft, wobei seine Geschwindigkeit unten von der Höhe abhängt, aus der es startet. Je höher die Rutsche, desto mehr potenzielle Energie hat das Wasser oben, die beim Herunterfließen in kinetische Energie umgewandelt wird, wodurch seine Geschwindigkeit zunimmt.

Das Bernoulli-Prinzip bestimmt die Geschwindigkeit des Wassers entlang der Rutsche. Das Prinzip setzt die potenzielle Energie an Punkt 1 (oben), die kinetische Energie an Punkt 2 (unten) und den Druck des Wassers an beiden Punkten in Beziehung.

<img alt="Equation 1" src="/files/ftp_upload/18040/18040_Equation_1.svg" style="text-align: center; height: 28px;">

Wenn das Wasser in einer Wasserrutsche bergab fließt, nimmt seine potenzielle Energie ab, während seine kinetische Energie zunimmt, was zu einer Geschwindigkeitssteigerung führt. Die Bernoulli-Gleichung geht von keiner Reibung aus und behandelt Wasser als ideale Flüssigkeit, d. h. es fließt ohne Energieverlust durch Reibung oder Turbulenzen. Diese Annahmen vereinfachen die Berechnungen, obwohl in realen Szenarien die Reibung die tatsächliche Geschwindigkeit des Wassers leicht reduzieren kann.

Am oberen Ende der Rutsche steht das Wasser fast still und beschleunigt beim Herunterrutschen. Wenn die Rutsche zu hoch ist, kann das Wasser am unteren Ende eine gefährliche Geschwindigkeit erreichen, was ein Risiko für die Benutzer darstellt. Daher ist es notwendig, die Höhe h der Rutsche anzupassen, um die Geschwindigkeit des Wassers innerhalb sicherer Grenzen zu halten. Durch Berechnung der geeigneten Höhe mithilfe des Bernoulli-Prinzips kann die Rutsche die Geschwindigkeit des Wassers reduzieren und gleichzeitig eine aufregende Fahrt bieten.

<img alt="Equation 2" src="/files/ftp_upload/18040/18040_Equation_2.svg" style="text-align: center; height: 36px;">

Designbeispiel: Design einer Wasserrutsche

Ein Ingenieur entwirft eine Wasserrutsche für einen Wasserpark, auf der Wasser nach unten fließt, um den Parkbesuchern eine schnelle und dennoch sichere Fahrt zu ermöglichen.
Die Rutsche ist 25 Meter lang ...

Education

Lehre

JoVE Core

Civil Engineering

Bauingenieurwesen

Unit 1

Einheit 1

Fluid Dynamics

Strömungsmechanik

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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

The Scientific Method

The scientific method is a detailed, empirical problem-solving process used by biologists and other scientists. This iterative approach involves ...

Inductive Reasoning

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Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

Correlation and Causation

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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.

Scientific Method

The scientific method is used to solve problems and explain phenomena. The development of the scientific method coincided with changes in philosophy ...

Demonstrating the Scientific Method with Tree Branches
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Observation and Background Research
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Problem Definition

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The researcher identifies and explains the specific issue or gap to be ...

Apply science practices related to specialized topics of study to plan and conduct investigations or use engineering practices to design solutions to problems;

112.51.c.1.B.

Proper Personal Protective Equipment

Robert M. Rioux &#38; William A Elliott, Pennsylvania State University, University Park, PA
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Emergency Eyewash and Shower Stations

Robert M. Rioux, Pennsylvania State University, University Park, PA
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Electrical Safety

Robert M. Rioux &amp; Suprita Jharimune, Pennsylvania State University, University Park, PA
Among the many hazards present in the laboratory, electrical ...

Working with Centrifuges

Source: Robert M. Rioux &amp; Suprita Jharimune, Pennsylvania State University, University Park, PA
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Working with Hot and Cold Sources

Source: Robert M. Rioux &amp; Suprita Jharimune, Pennsylvania State University, University Park, PA
Working with extreme temperatures, both high and low, ...

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Robert M. Rioux &amp; Zhifeng Chen, Pennsylvania State University, University Park, PA
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Chemical Storage: Categories, Hazards And Compatibilities

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Safe Handling of Mineral Acids

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Handling Chemical Spills

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Proper Use of Autoclaves

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Fume Hoods and Laminar Flow Cabinets

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Fume hoods and laminar flow cabinets are engineering controls ...

Decontamination for Laboratory Biosafety

Robert M. Rioux and Zhifeng Chen, Pennsylvania State University, University Park, PA
Decontamination is essential for laboratory biosafety, as the ...

Proper Waste Disposal

Robert M. Rioux and Taslima A. Zaman, Pennsylvania State University, Pennsylvania, PA

Users are responsible for the proper disposal of the waste ...

Use appropriate safety equipment and practices during laboratory, classroom, and field investigations as outlined in Texas Education Agency-approved safety standards;

112.51.c.1.C.

Common Lab Glassware and Uses

Source: Laboratory of Dr. Neal Abrams &#8212; SUNY College of Environmental Science and Forestry
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Proper Lab Notebook Keeping

Organic Lab Notebook Keeping
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Source: Lara Al Hariri at the University of Massachusetts Amherst, MA, USA

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Source: Lara Al Hariri and Ahmed Basabrain at the University of Massachusetts Amherst, MA, USA

	Nitration of Methyl BenzoateExpand
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112.51.c.1.D.

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International System of Units

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Measurement: Standard Units

Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement ...

Measurement: Derived Units

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, ...

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.

Review and Preview

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative ...

What is a Frequency Distribution

A frequency is the number of times a value of the data occurs. The sum of all the frequency values represents the total number of students included in the ...

Cumulative Frequency Distribution

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Ogive Graph

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Histogram

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Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. ...

Scatter Plot

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Time-Series Graph

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Bar Graph

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Multiple Bar Graph

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Pareto Chart

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Pie Chart

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Organize quantitative or qualitative data using representations appropriate to the specialized topic of study such as scatter plots, line graphs, bar graphs, charts, data tables, diagrams, scientific drawings, and student-prepared models;

112.51.c.1.F.

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Typical Model Studies

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112.51.c.1.G.

Scientific Laws and Theories

Scientific Laws

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Distinguish among scientific hypotheses, theories, and laws as appropriate to the specialized topic of study.

112.51.c.1.H.

Identify advantages and limitations of models such as their size, scale, properties, and materials as appropriate to the specialized topic of study;

112.51.c.2.A.

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Statistical Analysis: Overview

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Random Error

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Analyze data appropriate to the specialized topic of study by identifying significant statistical features, patterns, sources of error, and limitations;

112.51.c.2.B.

Numerical Calculations

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Significant Figures in Calculations

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Use mathematical calculations to assess quantitative relationships in data as appropriate to the specialized topic of study; and

112.51.c.2.C.

Scientific and engineering practices. The student, for at least 40% of instructional time, asks questions, identifies problems, and plans and safely conducts classroom, laboratory, and field investigations to explain phenomena or design solutions using appropriate tools and models. The student is expected to:

Water Slide Speed and Bernoulli's Principle

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