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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

The calculation of atmospheric pressure at the summit of Mount Everest carried out in Example 13.3 used the model known as the isothermal atmosphere, in which gas pressure is proportional to density: \(p=\gamma \rho\), with \(\gamma\) constant. Consider a spherical cloud of gas supporting itself under its own gravitation and following this model. a) Write the equation of hydrostatic equilibrium for the cloud, in terms of the gas density as a function of radius, \(\rho(r) .\) b) Show that \(\rho(r)=A / r^{2}\) is a solution of this equation, for an appropriate choice of constant \(A\). Explain why this solution is not suitable as a model of a star.

Salt water has a greater density than freshwater. A boat floats in both freshwater and salt water. The buoyant force on the boat in salt water is that in freshwater. a) equal to b) smaller than c) larger than

A wooden block floating in seawater has two thirds of its volume submerged. When the block is placed in mineral oil, \(80.0 \%\) of its volume is submerged. Find the density of the (a) wooden block, and (b) the mineral oil.

A scuba diver must decompress after a deep dive to allow excess nitrogen to exit safely from his bloodstream. The length of time required for decompression depends on the total change in pressure that the diver experienced. Find this total change in pressure for a diver who starts at a depth of \(d=20.0 \mathrm{~m}\) in the ocean (density of seawater \(\left.=1024 \mathrm{~kg} / \mathrm{m}^{3}\right)\) and then travels aboard a small plane (with an unpressurized cabin) that rises to an altitude of \(h=5000 . \mathrm{m}\) above sea level.

The average density of the human body is \(985 \mathrm{~kg} / \mathrm{m}^{3}\) and the typical density of seawater is about \(1020 \mathrm{~kg} / \mathrm{m}^{3}\) a) Draw a free-body diagram of a human body floating in seawater and determine what percentage of the body's volume is submerged. b) The average density of the human body, after maximum inhalation of air, changes to \(945 \mathrm{~kg} / \mathrm{m}^{3}\). As a person floating in seawater inhales and exhales slowly, what percentage of his volume moves up out of and down into the water? c) The Dead Sea (a saltwater lake between Israel and Jordan ) is the world's saltiest large body of water. Its average salt content is more than six times that of typical seawater, which explains why there is no plant and animal life in it. Two-thirds of the volume of the body of a person floating in the Dead Sea is observed to be submerged. Determine the density (in \(\mathrm{kg} / \mathrm{m}^{3}\) ) of the seawater in the Dead Sea.
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