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Chapter 13: Problem 14

In what direction does a force due to water flowing from a showerhead act on a shower curtain, inward toward the shower or outward? Explain.

Short Answer

Expert verified
Answer: The force acts on the shower curtain in the inward direction, towards the shower. This phenomenon occurs due to Bernoulli's principle and the Venturi effect, which state that as the air velocity increases in the space between the showerhead and the curtain, the air pressure decreases, leading to an inward force acting on the shower curtain.

Step by step solution

01

1. Identify the relevant forces

First, we need to identify the forces acting on the shower curtain due to the flowing water. These forces are primarily caused by the water's pressure and the surrounding air pressure.
02

2. Apply Bernoulli's equation

Bernoulli's equation relates the pressure, kinetic energy, and potential energy of a fluid in a system. In this case, we want to find out how the fluid pressure changes due to the motion of the water and apply that knowledge to the shower curtain.
03

3. The Venturi effect

According to Bernoulli's principle, as the fluid's velocity increases, its pressure decreases. The Venturi effect is a phenomenon that occurs when a fluid flows through a pipe with a constriction: The fluid's velocity increases in the narrower section and the pressure decreases. The same principle can be applied to the water and air flowing in the shower.
04

4. Force direction on a shower curtain

When water flows from the showerhead, it speeds up in the space between the showerhead and the shower curtain. This increase in the air velocity leads to a drop in air pressure near the curtain on the inside (shower side) relative to the air pressure outside the shower. This pressure difference causes the force to act on the shower curtain in an inward direction, towards the shower.
05

5. Conclusion

The force due to water flowing from a showerhead acts on a shower curtain in the inward direction, towards the shower. This phenomenon occurs because, according to Bernoulli's principle and the Venturi effect, as the air velocity increases in the space between the showerhead and the curtain, the air pressure decreases, leading to an inward force acting on the shower curtain.

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Most popular questions from this chapter

A water pipe narrows from a radius of \(r_{1}=5.00 \mathrm{~cm}\) to a radius of \(r_{2}=2.00 \mathrm{~cm} .\) If the speed of the water in the wider part of the pipe is \(2.00 \mathrm{~m} / \mathrm{s}\), what is the speed of the water in the narrower part?

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