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 ingegnere sta progettando uno scivolo acquatico per un parco acquatico, dove l'acqua scorre verso il basso per creare una corsa veloce ma sicura per i visitatori del parco.
Lo scivolo è lungo 25 metri e inizia ad un'altezza di 10 metri, con una velocità di sicurezza di 12 metri al secondo sul fondo.
L'equazione di Bernoulli aiuta a calcolare la velocità dell'acqua, mettendo in relazione l'energia potenziale, l'energia cinetica e la pressione in entrambi i punti aperti all'aria. Non presuppone alcun attrito e tratta l'acqua come un fluido ideale.
Nella parte superiore dello scivolo, l'acqua è a riposo e la sua velocità aumenta man mano che scende.
Con l'altezza dello scivolo di 10 metri, la velocità calcolata dell'acqua sul fondo è di circa 14 metri al secondo, che supera il limite di sicurezza.
L'altezza dello scivolo deve essere abbassata per ridurre la velocità a un livello di sicurezza.
Dopo aver ricalcolato per una velocità di 12 metri al secondo, l'altezza dello scivolo dovrebbe essere ridotta a circa 7,34 metri.
In questo modo si garantisce che l'acqua scorra lungo lo scivolo in modo sicuro, evitando che superi la velocità di sicurezza quando raggiunge il fondo.

esempio di progettazione: progettazione di uno scivolo d'acqua

Quando si progetta uno scivolo d'acqua, controllare la velocità del flusso d'acqua è fondamentale per la sicurezza dell’utente, pur rendendo al contempo l'esperienza emozionante. Quando l'acqua scorre lungo lo scivolo, la gravità ne provoca l'accelerazione, con la sua velocità alla base che dipende dall'altezza da cui parte. Più alto è lo scivolo, maggiore è l'energia potenziale che l'acqua possiede, che viene convertita in energia cinetica durante la discesa, aumentandone la velocità.

Il principio di Bernoulli, determina la velocità dell'acqua lungo lo scivolo. Il principio mette in relazione l'energia potenziale nel punto 1, in alto, l'energia cinetica nel punto 2, in basso, e la pressione dell'acqua in entrambi i punti.

<img alt="Equation 1" src="/files/ftp_upload/18040/18040_Equation_1.svg" style="text-align: center; height: 28px;">

In uno scivolo d'acqua, quando l'acqua si muove in discesa, la sua energia potenziale diminuisce, mentre quella cinetica aumenta, determinando un aumento della velocità. L'equazione di Bernoulli presuppone l'assenza di attrito e tratta l'acqua come un fluido ideale, il che significa che scorre senza perdite di energia dovute ad attrito o turbolenze. Queste ipotesi semplificano i calcoli, anche se in scenari reali, l'attrito potrebbe ridurre leggermente la velocità effettiva dell'acqua.

In cima allo scivolo, l'acqua è quasi ferma e, mentre scende, accelera. Se lo scivolo è troppo alto, l'acqua può raggiungere velocità pericolose nella parte inferiore, mettendo a rischio la sicurezza degli utilizzatori. Pertanto, è necessario regolare l'altezza h dello scivolo, per mantenere la velocità dell'acqua entro limiti di sicurezza. Calcolando l'altezza appropriata utilizzando il principio di Bernoulli, lo scivolo può ridurre la velocità dell'acqua, offrendo al contempo una corsa emozionante.

<img alt="Equation 2" src="/files/ftp_upload/18040/18040_Equation_2.svg" style="text-align: center; height: 36px;">

Esempio di Progettazione: Progettazione di uno Scivolo d'Acqua

Un ingegnere sta progettando uno scivolo acquatico per un parco acquatico, dove l'acqua scorre verso il basso per creare una corsa veloce ma sicura per i visitatori del parco.
Lo scivolo è di 25 metri...

Education

Didattica

JoVE Core

Civil Engineering

Ingegneria Civile

Unit 1

Unità 1

Fluid Dynamics

Dinamica dei fluidi

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

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

Correlation and CausationStatistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. A ...

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
ExpandObtain branches containing a few dozen typical leaves from five different local tree species. ...

Observation and Background Research
ExpandNOTE: The first two steps in the scientific process involve studying and observing natural phenomena of ...

Problem-Solving

A problem-solving strategy is a plan of action used to find a solution. It involves trial and error, algorithms, heuristics, and insights. Effective ...

Problem Definition

Problem definition is the initial and the most essential step in research.
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
Hazards are many and varied in the laboratory, but the right ...

Emergency Eyewash and Shower Stations

Robert M. Rioux, Pennsylvania State University, University Park, PA
The Occupational Safety and Health Administration (OSHA) mandates that an emergency ...

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
Earth's gravitational force is capable of separating ...

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, ...

guidelines-in-case-of-a-laboratory-emergency

Guidelines in Case of a Laboratory Emergency

Robert M. Rioux &amp; Zhifeng Chen, Pennsylvania State University, University Park, PA
The most common laboratory emergencies include chemical spills, ...

chemical-storage-categories-hazards-and-compatibilities

Chemical Storage: Categories, Hazards And Compatibilities

Source: Robert M. Rioux &amp; Taslima A. Zaman, Pennsylvania State University, University Park, PA
While the use of various chemicals in experimental ...

Safe Handling of Mineral Acids

Source: Robert M. Rioux &#38; Taslima A. Zaman, Pennsylvania State University, University Park, PA
A mineral acid (or inorganic acid) is defined as a ...

Handling Chemical Spills

Source: Robert M. Rioux &#38; Taslima Zaman, Pennsylvania State University, University Park, PA
Since chemicals are commonly used for laboratory research ...

Proper Use of Autoclaves

Robert M. Rioux &amp; Zhifeng Chen, Pennsylvania State University, University Park, PA
Autoclaving is one of the most commonly used methods in the ...

Fume Hoods and Laminar Flow Cabinets

Robert M. Rioux &amp; William A. Elliott, Pennsylvania State University, University Park, PA
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
Glassware is a regular appearance in the professional ...

Lab Techniques

Measurement Accuracy
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Source: Smaa Koraym at Johns Hopkins University, MD, USA

	Preparation of LaboratoryExpand
	Here we show the laboratory preparation for 10 students ...

Source: Smaa Koraym at Johns Hopkins University, MD, USA

	Determining the Density of an EggExpand
	Density is a measure of how compact a substance or ...

Proper Lab Notebook Keeping

Organic Lab Notebook Keeping
Record keeping is a vital skill in science and organic chemistry labs. Without proper notes, descriptions, quantities, or ...

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

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation ...

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

	Nitration of Methyl BenzoateExpand
	From this lab onward, ...

Use tools appropriate to the specialized topic of study;

112.51.c.1.D.

SI Units: 2019 Redefinition

Measurement is integral to analytical chemistry. Each record comprises a number &#8211; denoting the magnitude&#160; &#8211; and the unit &#8211; a ...

International System of Units

The International System of Units, known as the SI system, is a universally accepted measurement system recognized and used worldwide. The SI system is ...

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

A cumulative frequency distribution is another type of frequency distribution. Instead of reporting how many data values fall in some classes, it reports ...

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

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

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a ...

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct ...

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show ...

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can ...

Pareto Chart

A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the ...

Pie Chart

A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each ...

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.

Modeling and Similitude

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This setup predicts the ...

Typical Model Studies

Typical model studies analyze scaled-down systems to predict fluid behavior, focusing on interactions with free surfaces and flow around immersed bodies.
...

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Design Example: Creating a Hydraulic Model of a Dam Spillway

A hydraulic model of a dam spillway is often created by scaling down the design, typically to a 1:15 ratio, to replicate key flow characteristics such as ...

Models, Theories, and Laws

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Concepts and Prototypes

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Molecular Models

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Develop and use models to represent phenomena, systems, processes, or solutions to problems as appropriate to the specialized topic of study; and

112.51.c.1.G.

Scientific Laws and Theories

Scientific Laws

In science, a law is defined as a concise, verbal or mathematical, statement that summarizes a vast number of experimental observations. ...

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.

Introduction to Statistics

The science of statistics involves collecting, analyzing, interpreting, and presenting data. The method of collecting, organizing, and summarizing data is ...

Statistical Analysis: Overview

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

systematic-error-methodological-and-sampling-errors

Systematic Error: Methodological and Sampling Errors

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Random Error

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Types of Errors: Detection and Minimization

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Realism in Experimentation

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Bias

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Ethics in Research

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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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