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

يقوم مهندس بتصميم زلاجة مائية لحديقة مائية ، حيث تتدفق المياه لأسفل لخلق رحلة سريعة وآمنة لزوار الحديقة.
يبلغ طول الشريحة 25 مترا وتبدأ على ارتفاع 10 أمتار ، وتبلغ سرعتها الآمنة 12 مترا في الثانية في الأسفل.
تساعد معادلة برنولي في حساب سرعة الماء ، وربط الطاقة الكامنة والطاقة الحركية والضغط في كلتا النقطتين المفتوحتين للهواء. لا يفترض أي احتكاك ويعامل الماء كسائل مثالي.
في الجزء العلوي من الشريحة ، يكون الماء في حالة راحة ، وتزداد سرعته مع نزوله.
مع ارتفاع الشريحة 10 أمتار ، تبلغ السرعة المحسوبة للمياه في القاع حوالي 14 مترا في الثانية ، وهو ما يتجاوز الحد الآمن.
يجب خفض ارتفاع الشريحة لتقليل السرعة إلى مستوى آمن.
بعد إعادة الحساب لسرعة 12 مترا في الثانية ، يجب تقليل ارتفاع الشريحة إلى حوالي 7.34 متر.
هذا يضمن تدفق المياه إلى أسفل الشريحة بأمان ، مما يمنعها من تجاوز السرعة الآمنة عند وصولها إلى القاع.

مثال على التصميم: تصميم منزلق مائي.

<div style="direction:rtl">عند تصميم منزلق مائي، يمثل التحكم في سرعة تدفق المياه أمرًا بالغ الأهمية للحفاظ على سلامة المستخدمين اثناء استمتاعهم بتلك التجربة. فمع تدفق المياه نحو أسفل المنزلق، تتسبب الجاذبية في زيادة تسارعه، وتعتمد سرعته عند الأسفل على الارتفاع الذي يبدأ منه. تزداد طاقة الوضع للماء في الأعلى كلما زاد ارتفاع المنزلق، والتي يتم تحويلها إلى طاقة حركية أثناء نزول الماء، وهو ما يزيد من سرعته. يستخدم مبدأ برنولي في حساب سرعة الماء على امتداد المنزلق. ويربط المبدأ بين كل من طاقة الوضع عند القمة عند النقطة 1، وطاقة الحركة عند القاع عند النقطة 2، وضغط الماء عند كلتا النقطتين. <img alt="Equation 1" src="/files/ftp_upload/18040/18040_Equation_1.svg" style="text-align: center; height: 28px;"> في المنزلق المائي، مع تحرك الماء إلى اسفل المنزلق، تقل طاقة الوضع بالماء بينما تزداد طاقة الحركة، مما يؤدي إلى زيادة السرعة. تفترض معادلة برنولي عدم وجود قوى احتكاك وتتعامل مع الماء باعتباره مائعا مثاليًا، مما يعني أنه يتدفق دون فقدان للطاقة بسبب الاحتكاك أو اضطراب السريان. هذه الافتراضات على تبسيط الحسابات. على الرغم من أن الاحتكاك قد يقلل قليلاً من السرعة الفعلية للمياه في السيناريوهات الواقعية. في الجزء العلوي من المنزلق، يكون المياه في حالة سكون تقريبًا، ومع نزوله، تزداد سرعته. إذا كان ارتفاع المنزلق عاليأ جدًا، فقد تصل سرعة المياه في الاسفل إلى مستويات غير آمنة ، مما يشكل مخاطر على المستخدمين. لذلك، يعد ضبط ارتفاع المنزلق h ضروريًا لابقاء سرعة المياه ضمن الحدود الآمنة. باستخدام مبدأ برنولي يتم حساب الارتفاع المناسب الذي يسمح للمنزلق بتقليل سرعة المياه للحفاظ على سلامة المستخدمين. <img alt="Equation 2" src="/files/ftp_upload/18040/18040_Equation_2.svg" style="text-align: center; height: 36px;"></div>

يقوم مهندس بتصميم زلاجة مائية لحديقة مائية ، حيث تتدفق المياه لأسفل لخلق رحلة سريعة وآمنة لزوار الحديقة.
الشريحة 25 مترا ...

Education

JoVE Core

Civil Engineering

الهندسة المدنية

Unit 1

الوحدة الأولى

Fluid Dynamics

ديناميكا السوائل

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الرئيسية

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

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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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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.

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Emergency Eyewash and Shower Stations

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Proper Waste Disposal

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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.

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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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Histogram

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Relative Frequency Histogram

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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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112.51.c.1.G.

Scientific Laws and Theories

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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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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.

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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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