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Conceptual Physical Science 5th Edition Chapter 5: FLUID MECHANICS © 2012 Pearson Education, Inc. © 2012 Pearson Education, Inc. This lecture will help you understand: • • • • • • • • • Density Pressure Buoyancy in a Liquid Archimedes’ Principle Pressure in a Gas Atmospheric Pressure Pascal’s Principle Buoyancy in a Gas Bernoulli’s Principle © 2012 Pearson Education, Inc. Density Density • Important property of materials (solids, liquids, gases) • Measure of compactness of how much mass an object occupies • “lightness” or “heaviness” of materials of the same size © 2012 Pearson Education, Inc. Density • Equation : density = mass volume • Units of: – mass in grams or kilograms – volume in cm3 or m3 – density in kg/m3 or g/cm3 Example: The density of mercury is 13.6 g/cm3, so mercury has 13.6 times as much mass as an equal volume of water (density 1 g/cm3). © 2012 Pearson Education, Inc. Density Weight density • in equation form: weight density = weight volume often expressed in pounds per cubic foot example: density of salt water is 64 lb/ft3, more dense than fresh water (density 62.4 lb/ft3) © 2012 Pearson Education, Inc. Density CHECK YOUR NEIGHBOR Which of these has the greatest density? A. B. C. D. 100 kg of lead 100 kg of water Both are the same None of the above © 2012 Pearson Education, Inc. Density CHECK YOUR ANSWER Which of these has the greatest density? A. B. C. D. 100 kg of lead 100 kg of water Both are the same None of the above Explanation: They have the same mass and weight, but different volumes. Any amount of lead is more dense than any amount of water. © 2012 Pearson Education, Inc. Pressure • force per unit area that one object exerts on another • equation: pressure = force area • depends on area over which force is distributed • units in lb/ft2, N/m2, or Pa (Pascals) © 2012 Pearson Education, Inc. Pressure in a Liquid • Force per unit area that a liquid exerts on something • Depth dependent and not volume dependent Example: Swim twice as deep and the pressure due to the weight of water above you is twice as much. (For total pressure, add to this the atmospheric pressure acting on the water surface.) © 2012 Pearson Education, Inc. Pressure in a Liquid Effects of water pressure • acts perpendicular to surfaces of a container • liquid spurts at right angles from a hole in the surface curving downward – The greater the depth, the greater the exiting speed © 2012 Pearson Education, Inc. Pressure in a Liquid • Acts equally in all directions Examples: • your ears feel the same amount of pressure under water no matter how you tip your head • bottom of a boat is pushed upward by water pressure • pressure acts upward when pushing a beach ball under water © 2012 Pearson Education, Inc. Pressure in a Liquid • Independent of shape of container whatever the shape of a container, pressure at any particular depth is the same • Equation: liquid pressure = weight density depth © 2012 Pearson Education, Inc. Water Tower • Force of gravity acting on the water in a tall tower produces pressure in pipes below that supply many homes with reliable water pressure. © 2012 Pearson Education, Inc. Pressure CHECK YOUR NEIGHBOR Suppose water from a tall tower supplies a nearby home. If water faucets upstairs and downstairs are turned fully on, will more water per second flow from the downstairs or the upstairs faucet? Or will water flow in each be the same? A. B. C. D. Downstairs. Upstairs. Same. Not enough information in problem. © 2012 Pearson Education, Inc. Pressure CHECK YOUR ANSWER Suppose water from a tall tower supplies a nearby home. If water faucets upstairs and downstairs are turned fully on, will more water per second flow from the downstairs or the upstairs faucet? Or will water flow in each be the same? A. B. C. D. Downstairs Upstairs Same Not enough information in problem. Explanation: Water pressure depends on the depth below the free surface. Downstairs faucets are simply “deeper” and receive greater pressure, which means greater rate of water flow. © 2012 Pearson Education, Inc. Pressure CHECK YOUR NEIGHBOR Does a 3-meter deep lake or a 6-meter deep small pond exert more pressure on a dam? A. B. C. D. The three-meter deep lake. The six-meter deep small pond. Same amount of pressure is exerted (atmospheric) so same force. Not enough information given in the question. © 2012 Pearson Education, Inc. Pressure CHECK YOUR ANSWER Does a 3-meter deep lake or a 6-meter deep small pond exert more pressure on a dam? A. B. C. D. The three-meter deep lake. The six-meter deep small pond. Same amount of pressure is exerted (atmospheric) so same force. Not enough information given in the question. © 2012 Pearson Education, Inc. Buoyancy in a Liquid Buoyancy • apparent loss of weight of a submerged object • amount equals the weight of water displaced © 2012 Pearson Education, Inc. Archimedes’ Principle Archimedes’ Principle • discovered by Greek scientist Archimedes • relates buoyancy to displaced liquid • states that an immersed body (completely or partially) is buoyed up by a force equal to the weight of the fluid it displaces • applies to gases and liquids © 2012 Pearson Education, Inc. Archimedes’ Principle Apparent weight of a submerged object • weight out of water – buoyant force Example: if a 3-kg block submerged in water apparently “weighs” 1 kg, then the buoyant force or weight of water displaced is 2 kg (BF = wt out of water – apparent wt = 3 kg – 1 kg = 2 kg) © 2012 Pearson Education, Inc. Archimedes’ Principle • Displacement rule: A completely submerged object always displaces a volume of liquid equal to its own volume. Example: Place a stone in a container that is brim- full of water, and the amount of water overflow equals the volume of the stone © 2012 Pearson Education, Inc. Archimedes’ Principle • Buoyant force is equal to the weight of fluid displaced. It can also be understood by pressure differences. • The greater pressure against the bottom of the box, minus the pressure on the top, results in an upward force—the buoyant force. © 2012 Pearson Education, Inc. Archimedes’ Principle Buoyant Force • Buoyant force is equal to the weight of fluid displaced. • Understood by pressure differences greater pressure against the box – pressure on the top of box © 2012 Pearson Education, Inc. Archimedes’ Principle CHECK YOUR NEIGHBOR On which of these blocks submerged in water is the buoyant force greatest? A. B. C. D. 1 kg of lead. 1 kg of aluminum. 1 kg of uranium. All the same. © 2012 Pearson Education, Inc. Archimedes’ Principle CHECK YOUR ANSWER On which of these blocks submerged in water is the buoyant force greatest? A. B. C. D. 1 kg of lead. 1 kg of aluminum. 1 kg of uranium. All the same. Explanation: The largest block is the aluminum one. It displaces more water and therefore experiences the greatest buoyant force. © 2012 Pearson Education, Inc. Archimedes’ Principle Flotation • Principle of flotation – A floating object displaces a weight of fluid equal to its own weight Example: A solid iron 1-ton block may displace 1/8 ton of water and sink. The same 1 ton of iron in a bowl shape displaces a greater volume of water—the greater buoyant force allows it to float © 2012 Pearson Education, Inc. Archimedes’ Principle CHECK YOUR NEIGHBOR The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water A. B. C. D. the buoyant force is greater. a person feels less heavy. a smaller volume of water is displaced. None of the above. © 2012 Pearson Education, Inc. Archimedes’ Principle CHECK YOUR ANSWER The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water A. B. C. D. the buoyant force is greater. a person feels less heavy. a smaller volume of water is displaced. None of the above. Explanation: A floating person has the same buoyant force whatever the density of water. A person floats higher because a smaller volume of the denser salt water is displaced. © 2012 Pearson Education, Inc. Archimedes’ Principle CHECK YOUR NEIGHBOR On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoamfilled preservers. A. B. He apparently doesn’t know his physics. He is correct. © 2012 Pearson Education, Inc. Archimedes’ Principle CHECK YOUR ANSWER On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoamfilled preservers. A. B. He apparently doesn’t know his physics. He is correct. Explanation: He’s correct, but what he doesn’t tell you is you’ll drown! Your life preserver will submerge and displace more water than those of your friends who float at the surface. Although the buoyant force on you will be greater, the net force downward is greater still! © 2012 Pearson Education, Inc. Pressure in a Gas The Falkirk Wheel in Scotland illustrates Figure 5.17 in your book. Each of the two caissons weigh the same regardless of the weights of floating boats they carry. © 2012 Pearson Education, Inc. Pressure in a Gas • Gas pressure is a measure of the amount of force per area that a gas exerts against containing walls. • Here the force is exerted by the motion of molecules bouncing around. • Temperature is a measure of the KE per molecules of the gas. © 2012 Pearson Education, Inc. Pressure in a Gas Relationship between pressure and density • Gas pressure is proportional to density Example: – Air pressure and air density inside an inflated tire are greater than the atmospheric pressure and density outside – Twice as many molecules in the same volume air density doubled – For molecules moving at the same speed (same temperature), collisions are doubled pressure doubled © 2012 Pearson Education, Inc. Pressure in a Gas Double density of air by • Doubling the amount of air • Decreasing the volume to half © 2012 Pearson Education, Inc. Pressure in a Gas Boyle’s Law • Relationship between pressure and volume for ideal gases • An ideal gas is one in which intermolecular forces play no role • States that pressure volume is a constant for a given mass of confined gas regardless of changes in pressure or volume (with temperature remaining unchanged) • pressure volume = constant means that P1V1 = P2V2 © 2012 Pearson Education, Inc. Pressure in a Gas CHECK YOUR NEIGHBOR When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon A. B. C. D. is 0.8 its former pressure. remains the same if you squeeze it slowly. is 1.25 times greater. is 8 times greater. © 2012 Pearson Education, Inc. Pressure in a Gas CHECK YOUR ANSWER When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon A. B. C. D. is 0.8 its former pressure. remains the same if you squeeze it slowly. is 1.25 times greater. is 8 times greater. Explanation: Boyle’s law, sweet and simple: P(1.0 V) = 1.25 P(0.8 V). © 2012 Pearson Education, Inc. Earth’s Atmosphere Atmosphere • ocean of air • exerts pressure The Magdeburg-hemispheres demonstration in 1654 by Otto von Guericke showed the large magnitude of atmosphere’s pressure. © 2012 Pearson Education, Inc. Atmospheric Pressure Atmospheric pressure • • • • Caused by weight of air Varies from one locality to another Not uniform Measurements are used to predict weather conditions © 2012 Pearson Education, Inc. Atmospheric Pressure • Pressure exerted against bodies immersed in the atmosphere result from the weight of air pressing from above • At sea level is 101 kilopascals (101 kPa) • Weight of air pressing down on 1 m2 at sea level ~ 100,000 N, so atmospheric pressure is ~ 105 N/m2 © 2012 Pearson Education, Inc. Atmospheric Pressure • Pressure at the bottom of a column of air reaching to the top of the atmosphere is the same as the pressure at the bottom of a column of water 10.3 m high. • Consequence: the highest the atmosphere can push water up into a vacuum pump is 10.3 m • Mechanical pumps that don’t depend on atmospheric pressure don’t have the 10.3-m limit © 2012 Pearson Education, Inc. Mechanical Pump • When the piston is lifted, the intake valve opens and air moves in to fill the empty space. • When the piston is moved downward, the outlet valve opens and the air is pushed out. © 2012 Pearson Education, Inc. Barometers Barometer • Device to measure atmospheric pressure • Also determines elevation Aneroid barometer • Small portable instrument that measures atmospheric pressure • Calibrated for altitude, then an altimeter © 2012 Pearson Education, Inc. Atmospheric Pressure CHECK YOUR NEIGHBOR Atmospheric pressure is caused by the A. B. C. D. density of Earth’s atmosphere. weight of Earth’s atmosphere. temperature of the atmosphere. effect of the Sun’s energy on the atmosphere. © 2012 Pearson Education, Inc. Atmospheric Pressure CHECK YOUR ANSWER Atmospheric pressure is caused by the A. B. C. D. density of Earth’s atmosphere. weight of Earth’s atmosphere. temperature of the atmosphere. effect of the Sun’s energy on the atmosphere. © 2012 Pearson Education, Inc. Atmospheric Pressure CHECK YOUR NEIGHBOR Two people are drinking soda using straws. Do they suck the soda up? Could they drink a soda this way on the Moon? A. B. C. D. Yes and yes. No, they suck the air out and the atmospheric pressure pushes the soda up. Yes, they could do the same thing on the Moon. No, they reduce air pressure in the straw and the atmospheric pressure pushes the soda up. No, they could not do the same thing on the Moon. Yes. No, they could not do the same thing on the Moon. © 2012 Pearson Education, Inc. Atmospheric Pressure CHECK YOUR ANSWER Two people are drinking soda using straws. Do they suck the soda up? Could they drink a soda this way on the moon? A. B. C. D. Yes and yes. No, they suck the air out and the atmospheric pressure pushes the soda up. Yes, they could do the same thing on the Moon. No, they reduce air pressure in the straw and the atmospheric pressure pushes the soda up. No, they could not do the same thing on the Moon. Yes. No, they could not do the same thing on the Moon. © 2012 Pearson Education, Inc. The Moon does not have an atmosphere. Pascal’s Principle Pascal’s principle • Discovered by Blaise Pascal, a scientist and theologian in the 17th century • States that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid • Applies to all fluids—gases and liquids © 2012 Pearson Education, Inc. Pascal’s Principle • Application in hydraulic press Example: – Pressure applied to the left piston is transmitted to the right piston – A 10-kg load on small piston (left) lifts a load of 500 kg on large piston (right) © 2012 Pearson Education, Inc. Pascal’s Principle CHECK YOUR NEIGHBOR A 10-kg load on the left piston will support a 500-kg load on the right piston. How does the pressure of fluid against the lower part of the left piston compare with the pressure against the lower right piston? A. B. C. D. More pressure on the left piston. More pressure on the right piston. Same pressure on each. Same force on each. © 2012 Pearson Education, Inc. Pascal’s Principle CHECK YOUR ANSWER A 10-kg load on the left piston will support a 500-kg load on the right piston. How does the pressure of fluid against the lower part of the left piston compare with the pressure against the lower right piston? A. B. C. D. More pressure on the left piston. More pressure on the right piston. Same pressure on each. Same force on each. © 2012 Pearson Education, Inc. Pascal’s Principle P1 P2 F1 F2 A1 A2 P1 F1 A1 © 2012 Pearson Education, Inc. • Since the pressure in the fluid is the same at both ends of the tube, one can cleverly change the force and area to mechanically multiply each. • This principle underlies a lot! P2 F2 A2 Pascal’s Principle • Application for gases and liquids – seen in everyday hydraulic devices used in construction – in auto lifts in service stations • increased air pressure produced by an air compressor is transmitted through the air to the surface of oil in an underground reservoir. The oil transmits the pressure to the piston, which lifts the auto. (Here surface area of reservoir is irrelevant.) © 2012 Pearson Education, Inc. Pascal’s Principle CHECK YOUR NEIGHBOR In a hydraulic device, it is impossible for the A. B. C. D. output piston to move farther than the input piston. force output to exceed the force input. output piston’s speed to exceed the input piston’s speed. energy output to exceed energy input. © 2012 Pearson Education, Inc. Pascal’s Principle CHECK YOUR ANSWER In a hydraulic device, it is impossible for the A. B. C. D. output piston to move farther than the input piston. force output to exceed the force input. output piston’s speed to exceed the input piston’s speed. energy output to exceed energy input. Explanation: This illustrates the conservation of energy, a cornerstone of all of science. © 2012 Pearson Education, Inc. Buoyancy in a Gas • Archimedes’ principle applies to fluids—liquids and gases alike. • Force of air on bottom of balloon is greater than force on top. • Net horizontal forces cancel, but not vertical ones, which supplies the buoyant force. • And this buoyant force equals the weight of displaced air! © 2012 Pearson Education, Inc. Buoyant Force CHECK YOUR NEIGHBOR Is there a buoyant force acting on your classmates at this moment? Defend your answer. A. B. C. D. No. If there were, they would float upward. Yes, but it is insignificant compared with their weights. Only in water, but not in air. None of these. © 2012 Pearson Education, Inc. Buoyant Force CHECK YOUR ANSWER Is there a buoyant force acting on your classmates at this moment? Defend your answer. A. B. C. D. No. If there were, they would float upward. Yes, but it is insignificant compared with their weights. Only in water, but not in air. None of these. © 2012 Pearson Education, Inc. Fluid Flow Continuous flow • Volume of fluid that flows past any cross-section of a pipe in a given time is the same as that flowing past any other section of the pipe even if the pipe widens or narrows. • Fluid speeds up when it flows from a wide to narrow pipe • Motion of fluid follows imaginary streamlines © 2012 Pearson Education, Inc. Bernoulli’s Principle Bernoulli’s Principle • Discovered by Daniel Bernoulli, a 15th century Swiss scientist • States that where the speed of a fluid increases, internal pressure in the fluid decreases • Applies to a smooth, steady flow © 2012 Pearson Education, Inc. Bernoulli’s Principle Streamlines • Thin lines representing fluid motion • Closer together, flow speed is greater and pressure within the fluid is less (note the larger bubbles!) • Wider, flow speed is less and pressure within the fluid is greater (greater pressure squeezes bubbles smaller) © 2012 Pearson Education, Inc. Bernoulli’s Principle Laminar flow • Smooth steady flow of constant density fluid Turbulent flow • Flow speed above a critical point becomes chaotic © 2012 Pearson Education, Inc. Bernoulli’s Principle CHECK YOUR NEIGHBOR What happens to the internal water pressure in a narrowing pipe of moving water? A. B. C. D. Pressure is higher. Pressure remains unchanged. Pressure is less. None of these. © 2012 Pearson Education, Inc. Bernoulli’s Principle CHECK YOUR ANSWER What happens to the internal water pressure in a narrowing pipe of moving water? A. B. C. D. Pressure is higher. Pressure remains unchanged. Pressure is less. None of these. Explanation: This reduction in pressure would be apparent if air bubbles were in the flowing water. Note their sizes increase in the narrow part, due to reduced pressure there! © 2012 Pearson Education, Inc. Applications of Bernoulli • Moving air gains speed above the roof of a house. This change in air velocity means reduced pressure on the roof. • Therefore, air pressure inside the house is greater, which can raise the roof. © 2012 Pearson Education, Inc. Bernoulli Application CHECK YOUR NEIGHBOR The pressure in a stream of water is reduced as the stream speeds up. How then can a stream of water from a fire hose actually knock a person off his or her feet? A. B. C. D. It can’t, as Bernoulli’s principle illustrates. The pressure due to water’s change in momentum can be much greater than the water’s internal pressure. Bernoulli’s principle works only for laminar flow, which the stream is not. None of the above. © 2012 Pearson Education, Inc. Bernoulli Application CHECK YOUR ANSWER The pressure in a stream of water is reduced as the stream speeds up. How then can a stream of water from a fire hose actually knock a person off his or her feet? A. B. C. D. It can’t, as Bernoulli’s principle illustrates. The pressure due to water’s change in momentum can be much greater than the water’s internal pressure. Bernoulli’s principle works only for laminar flow, which the stream is not. None of the above Explanation: There’s a basic distinction between the pressure within flowing water and the pressure it can exert when its momentum is changed. The pressure that knocks one off his or her feet is due to the change in the water’s momentum, not the pressure within the water. © 2012 Pearson Education, Inc. Airplane wing • The vertical vector represents the net upward force (lift) that results from more air pressure below the wing than above the wing. • The horizontal vector represents the air drag force. © 2012 Pearson Education, Inc. Bernoulli Application CHECK YOUR NEIGHBOR Air speeds up as it is blown across the top of the vertical tube. How does this affect the air pressure in the vertical tube, and what then occurs? A. B. C. D. The air jet pulls liquid up the tube. Liquid mysteriously rises in the tube. Reduced air pressure in the tube (due to Bernoulli) lets atmospheric pressure on the liquid surface push liquid up into the tube where it joins the jet of air in a mist. Liquid in the vessel somehow turns to mist. © 2012 Pearson Education, Inc. Bernoulli Application CHECK YOUR ANSWER Air speeds up as it is blown across the top of the vertical tube. How does this affect the air pressure in the vertical tube, and what then occurs? A. B. C. D. The air jet pulls liquid up the tube. Liquid mysteriously rises in the tube. Reduced air pressure in the tube (due to Bernoulli) lets atmospheric pressure on the liquid surface push liquid up into the tube where it joins the jet of air in a mist. Liquid in the vessel somehow turns to mist. © 2012 Pearson Education, Inc. Bernoulli Boats • When the speed of water increases between boats, Bernoulli must be compensated for or else the boats collide! © 2012 Pearson Education, Inc. Bernoulli Umbrella • Why does Nellie Newton blame Bernoulli for her predicament? © 2012 Pearson Education, Inc.