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.

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’s velocity within safe limits. By calculating the appropriate height using Bernoulli's principle, the slide can reduce the water’s speed while offering a thrilling ride.