16.8
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…
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's equation helps calculate the water'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'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'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.
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Q1: How does Bernoulli's equation apply to water slide design?
Bernoulli's equation relates potential energy at the top of the slide to kinetic energy at the bottom, accounting for pressure at both points. It assumes water behaves as an ideal fluid with no friction, allowing engineers to calculate water velocity at the bottom using bernoulli s equation for flow along a streamline. This relationship helps determine whether the slide height produces safe speeds for riders.
Q2: Why does water accelerate as it flows down a water slide?
As water descends the slide, gravity converts its potential energy into kinetic energy, causing acceleration. The higher the starting height, the more potential energy the water possesses at the top. This energy transformation increases the water's velocity as it moves downhill toward the bottom.
Q3: What happens if a water slide is designed too tall?
If the slide is too tall, water reaches unsafe speeds at the bottom, posing risks to riders. The excessive height generates too much potential energy, which converts to excessive kinetic energy and velocity. Engineers must adjust the slide height to keep water speed within safe limits while maintaining an exciting experience.
Q4: How can engineers reduce water speed on a water slide?
Engineers reduce water speed by lowering the slide's height, which decreases the potential energy available at the top. For example, reducing height from 10 meters to 7.34 meters lowers water velocity from 14 meters per second to the safe limit of 12 meters per second. This adjustment ensures rider safety without sacrificing the thrill of the ride.
Q5: What assumptions does Bernoulli's equation make about water in a slide?
Bernoulli's equation assumes water is an ideal fluid that flows without energy loss due to friction or turbulence. It also assumes no friction between water and the slide surface. While these simplifications enable accurate calculations, real-world scenarios may experience slightly reduced speeds due to actual friction effects.
Q6: What is the relationship between slide height and water velocity at the bottom?
Water velocity at the bottom increases with slide height because greater height means more potential energy converts to kinetic energy. Using Bernoulli's principle, a 10-meter slide produces approximately 14 meters per second, while a 7.34-meter slide produces 12 meters per second. This direct relationship allows engineers to calculate the exact height needed for target velocities.
Q7: Why is water treated as an ideal fluid in water slide design calculations?
Treating water as an ideal fluid simplifies calculations by eliminating friction and turbulence variables, making bernoulli equation problem solving applicable. This assumption allows engineers to quickly determine required slide dimensions for safe speeds. Although real water experiences minor friction losses, the ideal fluid model provides sufficiently accurate results for practical design purposes.