Conceptual Physics Fundamentals Chapter 7: FLUID MECHANICS This lecture will help you understand: Density Pressure Pressure in a Liquid Buoyancy in a Liquid Pressure in a Gas Atmospheric Pressure Pascal s Principle Buoyancy in a Gas Bernoulli s Principle Fluid Mechanics Men never do evil so cheerfully and completely as when they do so from religious conviction. Blaise Pascal 1
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 Density in equation form: density = volume mass units: grams or kilograms volume: cm 3 or m 3 example: density of mercury is 13.6 g/cm 3, so mercury has 13.6 times as much mass as an equal volume of water (density 1 g/cm 3 ) Density The volume of 1000 kg of water is A. 1 liter. B. slightly less than 1 liter. C. more than 1 liter. 2
Density The volume of 1000 kg of water is A. 1 liter. B. slightly less than 1 liter. C. more than 1 liter. Density Weight density in equation form: weight density = weight volume example: density of salt water is 64 lb/ft 3, more dense than fresh water (density 62.4 lb/ft 3 ) Density Which of these has the greatest density? A. 100 kg of lead B. 100 kg of water C. both are the same 3
Density Which of these has the greatest density? A. 100 kg of lead B. 100 kg of water C. both are the same Explanation: They have the same mass and weight, but any amount of lead is more dense than any amount of water. Density When water freezes, it expands. This tells us that the density of ice is A. less than the density of water. B. equal to the density of water. C. more than the density of water. Density When water freezes, it expands. This tells us that the density of ice is A. less than the density of water. B. equal to the density of water. C. more than the density of water. 4
Density Compared with the weight of water, the weight of a liter of ice is A. more. B. less. C. the same. Density Compared with the weight of water, the weight of a liter of ice is A. more. B. less. C. the same. Explanation When a liter of water freezes, its volume increases. To get a liter of ice you d have to shave part of it off to be the same size. So there is less water in a liter of ice. Pressure the force per unit area that one object exerts on another in equation form: pressure = force area depends on area over which force is distributed units: N/m 2, lb/ft 2, or Pa (Pascals) 5
Pressure example: The teacher between nails is unharmed because force is applied over many nails. Combined surface area of the nails results in a tolerable pressure that does not puncture the skin. Pressure When you stand on one foot instead of two, the force you exert on the floor is A. less. B. the same. C. more. Pressure When you stand on one foot instead of two, the force you exert on the floor is A. less. B. the same. C. more. Explanation: Distinguish between force and pressure! 6
Pressure When you stand on one foot instead of two, the pressure you exert on the floor is A. less. B. the same. C. more. Pressure When you stand on one foot instead of two, the pressure you exert on the floor is A. less. B. the same. C. more. Explanation: Twice as much, in fact! Pressure in a Liquid force per unit area that a liquid exerts on an object depth dependent and not volume dependent example: swim twice as deep, then twice as much weight of water above you produces as much pressure on you 7
Pressure in a Liquid acts equally in all directions example: 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 Pressure in a Liquid independent of shape of container whatever the shape of a container, pressure at any particular depth is the same in equation form: liquid pressure = weight density depth Pressure in a Liquid Water pressure provided by a water tower is greater if the tower A. is taller. B. holds more water. C. both A and B 8
Pressure in a Liquid Water pressure provided by a water tower is greater if the tower A. is taller. B. holds more water. C. both A and B Explanation: Only depth, not amount of water, contributes to pressure. 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 Buoyancy in a Liquid Buoyancy apparent loss of weight of a submerged object amount equals the weight of water displaced 9
Buoyancy in a Liquid 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 Buoyancy in a Liquid A cook who measures a specific amount of butter by placing it in a measuring cup with water in it is using the A. principle of buoyancy. B. displacement rule. C. concept of density. D. all of the above Buoyancy in a Liquid A cook who measures a specific amount of butter by placing it in a measuring cup with water in it is using the A. principle of buoyancy. B. displacement rule. C. concept of density. D. all of the above 10
Buoyancy in a Liquid Buoyant force net upward force that a fluid exerts on an immersed object = weight of water displaced example: the difference in the upward and downward forces acting on the submerged block is the same at any depth Buoyancy in a Liquid How many forces act on a submerged body at rest in a fluid? A. one buoyancy B. two buoyancy and the force due to gravity C. none in accord with the equilibrium rule, ΣF = 0 Buoyancy in a Liquid How many forces act on a submerged body at rest in a fluid? A. one buoyancy B. two buoyancy and the force due to gravity C. none in accord with the equilibrium rule, ΣF = 0 11
Buoyancy in a Liquid Sink or float? sink when weight of submerged object is greater than the buoyant force neither sink nor float when weight of a submerged object is equal to buoyant force object will remain at any level float when weight of submerged object is less than the buoyant force it would have when submerged when floating, buoyant force = weight of floating object 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 Apparent weight of a submerged object weight out of water buoyant force example: if a 3-kg block submerged in water apparently weighs 2 kg, then the buoyant force or weight of water displaced is 1 kg 12
On which of these blocks submerged in water is the buoyant force greatest? A. 1 kg of lead B. 1 kg of aluminum C. 1 kg of uranium D. all the same On which of these blocks submerged in water is the buoyant force greatest? A. 1 kg of lead B. 1 kg of aluminum C. 1 kg of uranium D. all the same Explanation: The largest block is the aluminum one. It displaces more water and therefore experiences the greatest buoyant force. When a fish expands its air bladder, the density of the fish A. decreases. B. increases. C. remains the same. 13
When a fish expands its air bladder, the density of the fish A. decreases. B. increases. C. remains the same. When a fish makes itself less dense, the buoyant force on it A. decreases. B. increases. C. remains the same. When a fish makes itself less dense, the buoyant force on it A. decreases. B. increases. C. remains the same. 14
When a fish decreases the size of its air bladder, the density of the fish A. decreases. B. increases. C. remains the same. When a fish decreases the size of its air bladder, the density of the fish A. decreases. B. increases. C. remains the same. When a submarine takes water into its ballast tanks, its density A. decreases. B. increases. C. remains the same. 15
When a submarine takes water into its ballast tanks, its density A. decreases. B. increases. C. remains the same. When a submerged submarine expels water from its ballast tanks, its density A. decreases. B. increases. C. remains the same. When a submerged submarine expels water from its ballast tanks, its density A. decreases. B. increases. C. remains the same. Explanation: This is how a submerged submarine is able to surface. 16
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 The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water A. the buoyant force is greater. B. a person feels less heavy. C. neither of these The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water A. the buoyant force is greater. B. a person feels less heavy. C. neither of these 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. 17
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. He apparently doesn t know his physics. B. He is correct. 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. He apparently doesn t know his physics. B. 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! denser fluids will exert a greater buoyant force on a body than less dense fluids of the same volume example: ship will float higher in salt water (density = 1.03 g/cm 3 ) than in fresh water (density = 1.00 g/cm 3 ) 18
applies in air the more air an object displaces, the greater the buoyant force on it if an object displaces its weight, it hovers at a constant altitude if an object displaces less air, it descends As you sit in class, is there a buoyant force acting on you? A. no, as evidenced by an absence of lift B. yes, due to displacement of air Archimedes Prinicple As you sit in class, is there a buoyant force acting on you? A. no, as evidenced by an absence of lift B. yes, due to displacement of air Explanation: There is a buoyant force on you due to air displacement, but much less than your weight. 19
Pressure in a Gas greater distance between molecules in a gas than in a liquid molecules in a gas are free from the cohesive forces Molecular motion of gas exerts pressure against a container. For large volumes of gas, gravitational forces limit size and determine shape. 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 Pressure in a Gas Double density of air by doubling the amount of air decreasing the volume to half 20
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 P 1 V 1 = P 2 V 2 Pressure in a Gas When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon A. is 0.8 its former pressure. B. remains the same if you squeeze it slowly. C. is 1.25 times greater. D. is 8 times greater. Pressure in a Gas When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon A. is 0.8 its former pressure. B. remains the same if you squeeze it slowly. C. is 1.25 times greater. D. is 8 times greater. Explanation: Boyle s law, sweet and simple: P(1.0 V) = 1.25 P(0.8 V). 21
Atmosphere ocean of air exerts pressure Earth s Atmosphere The Magdeburg-hemispheres demonstration in 1654 by Otto von Guericke showed the large magnitude of atmosphere s pressure. Atmospheric Pressure Atmospheric pressure caused by weight of air varies from one locality to another not uniform measurements are used to predict weather conditions 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 m 2 at sea level ~ 100,000 N, so atmospheric pressure is ~ 10 5 N/m 2 22
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 Atmospheric Pressure Barometer device to measure atmospheric pressure also determines elevation Aneroid barometer small portable instrument that measures atmospheric pressure calibrated for altitude, then an altimeter Atmospheric Pressure The maximum height to which water can be drunk through a straw A. is 10.3 m. B. is about 76 cm. C. has no limit. 23
Atmospheric Pressure The maximum height to which water can be drunk through a straw A. is 10.3 m. B. is about 76 cm. C. has no limit. Explanation: However strong your lungs may be, or whatever device you use to make a vacuum in the straw, at sea level, the water could not be pushed up by the atmosphere higher than 10.3 m. Pascal s Principle Pascal s principle discovered by Blaise Pascal, a scientist and theologian in the 17 th 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 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) 24
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. Pascal s Principle In a hydraulic device, it is impossible for the A. output piston to move farther than the input piston. B. force output to exceed the force input. C. output piston s speed to exceed the input piston s speed. D. energy output to exceed energy input. Pascal s Principle In a hydraulic device, it is impossible for the A. output piston to move farther than the input piston. B. force output to exceed the force input. C. output piston s speed to exceed the input piston s speed. D. energy output to exceed energy input. 25
Buoyancy in a Gas Archimedes principle applies to air as well as liquids. states that an object surrounded by air is buoyed up by a force equal to the weight of the air displaced Buoyancy in Gas A dirigible that hovers in air A. displaces its volume of air. B. displaces its weight of air. C. both A and B D. neither A nor B Buoyancy in Gas A dirigible that hovers in air A. displaces its volume of air. B. displaces its weight of air. C. both A and B D. neither A nor B Explanation: Like a fish in water, both volume and weight of a fluid are displaced. 26
Buoyancy in Gas Rule for lighter-than-air objects: When the weight of air displaced by an object is greater than the weight of the object, it rises. When the weight of air displaced by an object equals the weight of the object, it hovers in air. When the weight of air displaced by an object is less than the weight of the object, it is not supported by air. Buoyancy in Gas Gas-filled balloons gas prevents atmosphere from collapsing them best buoyancy with hydrogen, the lightest gas (flammable, so seldom used) next-best buoyancy with helium heated air used in sports balloons As balloons rise, atmosphere becomes less dense with altitude. Buoyancy in Gas Gas-filled balloon will continue to rise until the weight of displaced air equals the total weight of the balloon the buoyant force on the balloon equals its weight (which says the same thing) 27
Buoyancy in Gas As a balloon rises higher and higher into the atmosphere, its A. volume decreases. B. density increases. C. weight increases. Buoyancy in Gas As a balloon rises higher and higher into the atmosphere, its A. volume decreases. B. density increases. C. weight increases. 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 pipe widens or narrows. fluid speeds up when it flows from a wide to narrow pipe motion of fluid follows imaginary streamlines 28
Bernoulli s Principle Bernoulli s Principle discovered by Daniel Bernoulli, a 15 th century Swiss scientist states that where the speed of a fluid increases, internal pressure in the fluid decreases applies to a smooth, steady flow Bernoulli s Principle Streamlines thin lines representing fluid motion closer together, flow speed is greater and pressure within the fluid is less wider, flow speed is less and pressure within the fluid is greater Bernoulli s Principle Laminar flow smooth steady flow of constant density fluid Turbulent flow flow speed above a critical point becomes chaotic 29
Bernoulli s Principle The pressure in a stream of water is reduced as the stream speeds up. Can a stream of water from a fire hose actually knock a person off his or her feet? A. It can t, as Bernoulli s principle illustrates. B. It can, and is consistent with Bernoulli s principle. C. Bernoulli s principle works only for laminar flow, which the stream is not. Bernoulli s Principle The pressure in a stream of water is reduced as the stream speeds up. Can a stream of water from a fire hose actually knock a person off his or her feet? A. It can t, as Bernoulli s principle illustrates. B. It can, and is consistent with Bernoulli s principle. C. Bernoulli s principle works only for laminar flow, which the stream is not. Explanation: There s a difference in 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. Bernoulli s Principle Applications of Bernoulli s Principle blow on the top surface of a paper and the paper rises reason: pressure of the moving air is less than the atmospheric pressure beneath it convertible car roof puffs upward as air moves over its top surface reason: pressure of air moving on the top surface is less than the atmospheric pressure inside the car 30
Bernoulli s Principle wind blowing across a peaked roof can lift the roof off the house reason: Pressure is reduced as wind gains speed as it flows over the roof. The greater pressure inside the house lifts the roof up. perfume atomizer reason: Air rushes across the open end of the tube when you squeeze the bulb, reducing pressure in the tube. Atmospheric pressure on the liquid below pushes it up into the tube. Bernoulli s Principle trucks passing closely on a highway are drawn to each other reason: air pressure between the trucks is less than pressure on their outer sides pushing inward risk of passing ships colliding sideways reason: water pressure between the ships is less than pressure on their outer sides pushing inward Bernoulli s Principle On a windy day, waves in a lake or the ocean are higher than their average height. What factor in Bernoulli s principle contributes to the increased height? A. Reduced pressure pulls water upward. B. Pressure builds up over the crests. C. Air travels faster over the crests than the troughs. 31
Bernoulli s Principle On a windy day, waves in a lake or the ocean are higher than their average height. What factor in Bernoulli s principle contributes to the increased height? A. Reduced pressure pulls water upward. B. Pressure builds up over the crests. C. Air travels faster over the crests than the troughs. Explanation: The troughs of the waves are partially shielded from the wind, so air travels faster over the crests. Pressure there is thus lower than down below in the troughs. The greater pressure in the troughs pushes water into the even higher crests. 32