Static Fluids How can a hot air balloon travel for hours in the sky? Why is it dangerous for scuba divers to ascend to the surface quickly from a deep-sea dive? Why does a 15-g nail sink in water and a cargo ship float? © 2014 Pearson Education, Inc.

Be sure you know how to: Draw a force diagram for a system of interest (Section 1.6). Apply Newton's second law in component form (Section 3.5). Define pressure (Section 9.2). © 2014 Pearson Education, Inc.

What's new in this chapter Previously, we constructed the ideal gas model and used it to explain the behavior of gases. –We ignored the effect of the gravitational force exerted by Earth on the gas particles. In this chapter, our interest expands to include phenomena in which the force exerted by Earth plays an important role. –We will confine the discussion to static fluids—fluids that are not moving. © 2014 Pearson Education, Inc.

Density To find the density of an object or a substance, determine its mass and volume and then calculate the ratio of the mass and volume: To find the volume of a solid object of irregular shape, submerge it in a graduated cylinder filled with water. © 2014 Pearson Education, Inc.

Density © 2014 Pearson Education, Inc.

Density and floating Helium-filled balloons accelerate upward in air, whereas air-filled balloons accelerate (slowly) downward. –The air-filled balloon must be denser than air. This situation is analogous to how a less dense liquid will float on a more dense liquid. © 2014 Pearson Education, Inc.

Solid water floats in liquid water The solid form of a particular substance is almost always denser than the liquid form of the same substance, with one very significant exception: liquid water and solid ice. –Because ice floats on liquid water, we can assume that the density of ice is less than that of water. –Ice has a lower density because in forming the crystal structure of ice, water molecules spread apart. © 2014 Pearson Education, Inc.

Pressure exerted by a fluid Take a water bottle and poke four holes at the same height along its perimeter. –Parabolic-shaped streams of water shoot out of the holes. –The water inside must push out perpendicular to the wall of the bottle, just as gas pushes out perpendicular to the wall of a balloon. –Because the four streams are identically shaped, the pressure at all points at the same depth in the fluid is the same. © 2014 Pearson Education, Inc.

Pascal's first law © 2014 Pearson Education, Inc.

Pascal's first law at a microscopic level Particles inside a container move randomly in all directions. When we push harder on one of the surfaces of the container, the fluid becomes compressed. The molecules near that surface collide more frequently with their neighbors, which in turn collide more frequently with their neighbors. The extra pressure exerted at one surface quickly spreads, such that soon there is increased pressure throughout the fluid. © 2014 Pearson Education, Inc.

Glaucoma A person with glaucoma has closed drainage canals. The buildup of fluid causes increased pressure throughout the eye, including at the retina and optic nerve, which can lead to blindness. © 2014 Pearson Education, Inc.

Hydraulic lift Pressure changes uniformly throughout the liquid, so the pressure under piston 2 is the same as the pressure under piston 1 if they are at the same elevation. © 2014 Pearson Education, Inc.

Pressure variation with depth Is the pressure the same throughout a vertical column of fluid? –If the pressure is the same, we should observe water coming out at the same arcs, as shown in Figure 10.7a. However, what we actually observe is Figure 10.7b. –Which assumptions might we need to reconsider to reconcile this observation with Pascal's first law? © 2014 Pearson Education, Inc.

Pressure variation with depth From the observed patterns, we reason that the pressure of the liquid at the hole depends only on the height of the liquid above the hole, and not on the mass of the liquid above. We also see that the pressure at a given depth is the same in all directions. Pascal's first law fails to explain this pressure variation at different depths below the surface. © 2014 Pearson Education, Inc.

Why does pressure vary at different levels? The top surface of the bottom book in the stack must balance the force exerted by the nine books above it plus the pressure force exerted by the air on the top book. The pressure increases on the top surface of each book in the stack as we go lower in the stack. © 2014 Pearson Education, Inc.

Testing our model of pressure in a liquid The model predicts that some water will come out of the bottle when we remove one tack, but that the leaking will soon stop. –This is exactly what happens when we perform the experiment. © 2014 Pearson Education, Inc.

How can we quantify pressure change with depth? © 2014 Pearson Education, Inc.

Tip When using Pascal's second law [Eq. (10.3)], picture the situation. Be sure to include a vertical y-axis that points upward and has a defined origin, or zero point. Then choose the two points of interest and identify their vertical y-positions relative to the axis. This lets you relate the pressures at those two points. © 2014 Pearson Education, Inc.

Quantitative Exercise 10.4 If your ears did not pop, then what would be the net force exerted by the inside and outside air on your eardrum at the top of a 1000-m-high mountain? You start your hike from sea level. The area of your eardrum is 0.50 cm 2. The density of air at sea level at normal conditions is 1.3 kg/m 3. The situation at the start of the hike, y 1 = 0, and at the end of the hike, y 2 = 1000 m, is sketched here. © 2014 Pearson Education, Inc.

Measuring atmospheric pressure Its been known since Galileo's time that a pump consisting of a piston in a long cylinder that pulls up water can lift water only 10.3 m. © 2014 Pearson Education, Inc.

Measuring atmospheric pressure Consider the pressure at three places: –The pressure at point 1 is atmospheric pressure. –The pressure at point 2, according to Pascal's second law, is also atmospheric pressure. –We assume that the pressure at point 3 is zero because the water is at a maximum height. © 2014 Pearson Education, Inc.

Measuring atmospheric pressure Using Eq. (10.3) with a change in height of 10.3 m gives exactly the value of atmospheric pressure. © 2014 Pearson Education, Inc.

Testing experiment © 2014 Pearson Education, Inc.

Testing experiment © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

The magnitude of the force of fluid on a submerged object The force exerted by the fluid pushing up on the bottom is greater than the force exerted by the fluid pushing down on the top of the block. © 2014 Pearson Education, Inc.

The magnitude of the force of fluid on a submerged object To calculate the magnitude of the upward buoyant force exerted by the fluid on the block, we use Eq. (10.3) to determine the upward pressure of the fluid on the bottom surface of the block, compared to the downward pressure of the fluid on the top surface of the block. © 2014 Pearson Education, Inc.

Archimedes' principle: The buoyant force © 2014 Pearson Education, Inc.

Tip © 2014 Pearson Education, Inc.

Buoyancy: Putting it all together © 2014 Pearson Education, Inc.

How do submarines manage to sink and then rise in the water? A submarine's density increases when water fills its compartments. –With enough water in the compartments, the submarine's density is greater than that of the water outside, and it sinks. When the water is pumped out, the submarine's density decreases. –With enough air in the compartments, its density is less than that of the outside water, and the submarine rises toward the surface. © 2014 Pearson Education, Inc.

Stability of ships A challenge to building watercraft is to maintain stable equilibrium for the ship, allowing it to right itself if it tilts to one side due to wind or rough seas. © 2014 Pearson Education, Inc.

Ballooning Using hot air, balloonists can adjust the average density of the balloon (e.g., the balloon's material, people, equipment) to match the density of air so that the balloon can float at any location in the atmosphere (up to certain limits). –A burner under the opening of the balloon regulates the temperature of the air inside the balloon and hence its volume and density. –This allows control over the buoyant force that the outside cold air exerts on the balloon. © 2014 Pearson Education, Inc.

Effects of altitude on humans The pressure of atmospheric air decreases as one moves higher and higher in altitude. © 2014 Pearson Education, Inc.

Effects of altitude on humans –Between 4600 m and 6000 m, heart and breathing rates increase dramatically, and cognitive and sensory function and muscle control decline. –Between 6000 m and 8000 m, climbers undergo critical hypoxia, characterized by rapid loss of muscular control and loss of consciousness. © 2014 Pearson Education, Inc.

Scuba diving Scuba divers breathe compressed air. –While moving slowly downward, a diver adjusts the pressure outlet from the compressed-air tank to accumulate gas from the cylinder into her lungs, increasing the internal pressure to balance the increasing external pressure. –If a diver returns too quickly to the surface, the great gas pressure in the lungs can force bubbles of gas into the bloodstream. –This gradual process is called decompression. © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.

Summary © 2014 Pearson Education, Inc.