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

An engineer is designing a waterslide for a water park, where water flows down to create a fast yet safe ride for park visitors.
The slide is 25 meters long and begins at a height of 10 meters, with a safe speed of 12 meters per second at the bottom.
Bernoulli&#39;s equation helps calculate the water&#39;s speed, relating the potential energy, kinetic energy, and pressure at both points that are open to air. It assumes no friction and treats water as an ideal fluid.
At the top of the slide, the water is at rest, and its velocity increases as it descends.
With the slide&#39;s height of 10 meters, the calculated speed of the water at the bottom is approximately 14 meters per second, which exceeds the safe limit.
The slide&#39;s height must be lowered to reduce the speed to a safe level.
After recalculating for a speed of 12 meters per second, the slide height should be reduced to approximately 7.34 meters.
This ensures that the water flows down the slide safely, preventing it from exceeding the safe speed as it reaches the bottom.

design example: designing water slide

When designing a water slide, controlling the speed of water flow is crucial for rider safety while maintaining an exciting experience. As water flows down the slide, gravity causes it to accelerate, with its speed at the bottom depending on the height from which it starts. The higher the slide, the more potential energy the water has at the top, which is converted into kinetic energy as it descends, increasing its speed.
Bernoulli's principle determines the water's velocity along the slide. The principle relates the potential energy at point 1, the top, the kinetic energy at point 2, the bottom, and the pressure of the water at both points.
<img alt="Bernoulli's equation, fluid dynamics, energy conservation, pressure, velocity, elevation, symbols." src="/files/ftp_upload/18040/18040_Equation_1.svg" style="text-align: center; height: 28px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
In a water slide, as the water moves downhill, its potential energy decreases while its kinetic energy increases, leading to an increase in velocity. Bernoulli's equation assumes no friction and treats water as an ideal fluid, meaning it flows without energy loss due to friction or turbulence. These assumptions simplify the calculations, though in real-world scenarios, friction may slightly reduce the actual speed of the water.
At the top of the slide, the water is nearly at rest, and as it descends, it accelerates. If the slide is too tall, the water can reach unsafe speeds at the bottom, posing risks to riders. Therefore, adjusting the slide's height h is necessary to keep the water&#8217;s velocity within safe limits. By calculating the appropriate height using Bernoulli's principle, the slide can reduce the water&#8217;s speed while offering a thrilling ride.
<img alt="Equation for static equilibrium, height calculation, potential energy, formula, physics concept." src="/files/ftp_upload/18040/18040_Equation_2.svg" style="text-align: center; height: 36px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />

An engineer is designing a waterslide for a water park, where water flows down to create a fast yet safe ride for park visitors.
The slide is 25 meters ...

Education

JoVE Core

Civil Engineering

Unit 1

Fluid Dynamics

KEY TERMS AND CONCEPTS

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...

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 offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

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.D.

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112.51.c.1.F.

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Scientific Laws and Theories

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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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