Fluids States of Matter Phase Changes Density Pressure Pascal's Principle Buoyant Force Archimedes' Principle Bernoulli's Principle Torricelli's principle Viscosity Turbulence Cohesion Adhesion Surface Tension
States of Matter Matter comes in a variety of states: solid, liquid, gas, and plasma. .The molecules of solid are locked in a rigid structure and can only vibrate. (Add thermal energy and the vibrations increase.) Some solids are crystalline, like table salt, in which the atoms are arranged in a repeating pattern. Some solids are amorphous, like glass, in which the atoms have no orderly arrangement. Either way, a solid has definite volume and shape . A liquid is virtually incompressible and has definite volume but no definite shape. (If you pour a liter of juice into several glasses, the shape of the juice has changed but the total volume hasn't.) . A gas is easily compressed. It has neither definite shape nor definite volume. (If a container of CO2 is opened, it will diffuse throughout the room.) A plasma is an ionized gas and is the most common form of matter in the universe, since the insides of stars are plasmas.
Phase Changes Evaporation: Liquid Gas Condensation: Gas ->Liquid Melting: Solid Liquid Freezing: Liquid - Solid Sublimation: Solid Gas A volatile liquid is one that evaporates quickly. Examples of sublimation: Dry ice (frozen CO2) goes directly from the solid to the gaseous state (it sublimates). This creates an eerie, old fashioned effect, like graveyard fog in a spooky, old monster movie. Comets are very small objects containing frozen gases that sublimate when the comet get close enough to the sun. This creates the characteristic tail the can be millions of miles long.
Fluids The term fluid refers to gases and liquids. Gases and liquids have re in common with each other than they do with solids, since gases and liquids both have molecules that are free to move around. They are not locked in place as they are in a solid. The hotter the fluid, the faster its molecules move on average, and the more space the fluid will occupy (if its container allows for expansion.) Also, unlike solids, fluids can flow. atoms/
Density Density is given by: The symbol for density is "rho." Density is simply mass per unit volume. Water, for example, has a density of about 1 gram per milliliter. (It varies slightly with temperature and pressure.) The S.I. unit for density is the kg/m3. For water: 1000 kg 1 g mL mL ..cm3 1 kg . 1000 g (100 cm)3 3
Pressure Pressure is given by: Pressure is simply force per unit area. Pressure is often measured in pounds per square inch (psi), atmospheres (atm), or torr (which is a millimeter of mercury). The S.I. unit for pressure is the pascal, which is a Newton per square meter: 1 Pa - 1 N/m2. Atmospheric pressure is at sea level is normally: 1 atm1.01 105 Pa 760 torr 14.7 psi. At the deepest ocean trench the pressure is about 110 million pascals.
Pressure in a Fluid Pressure in a fluid is the result of the forces exerted by molecules as they bounce off each other in all directions. Therefore, at a given depth in a liquid or gas, the pressure is the same and acts in every direction.
Pressure/ Density Questions 1. Why do snowshoes keep you from sinking into the snow? The snowshoes greatly increase the area over which your weight is distributed, thereby decreasing the pressure on the snow. 2. Why do swimmers float better in the ocean than in a lake? Because of the salt dissolved in it, seawater is about 2.5% denser, making people (and fish) more buoyant in it 3. Why don't they make longer snorkels so that people could dive deeper without scuba gear? The pressure difference just 6 m below water is great enough so that the air in the diver's lungs will be forced through the tube, collapsing his lungs. A shorter snorkel might not be fatal, but the pressure difference could prevent him from expanding his lungs (inhaling) 4. Which is denser, Earth or the sun? On average, Earth is denser, but the core of the sun is much denser than anything on Earth.
Pressure & Freezing For most liquids-but not water-the freezing point increases if its pressure is increased, i.e., it's easier to freeze most liquids if they're subjected to high pressures In order to turn a liquids into a solid, the molecules typically must get close enough together to form a crystal. Low temps mean slow moving molecules that are closer together, but high pressure can squeeze the molecules closer together, even if they're not moving very slowly. Water is an exception to this because, due to its molecular shape, it expands upon freezing. (Most other substances occupy more space as liquids than as solids.) So, squeezing water makes freezing it harder. The pressure on ice due to a passing skater can actually melt a small amount of the ice.
Pressure & Boiling The lower the pressure on a liquid, the easier it is to make it boil, i.e., as pressure increases, so does the boiling pt. This is because in order for a liquid to boil, molecules need enough kinetic energy to break free from the attraction of the molecules around it (Molecules with this much energy are in a gaseous state.) It's harder for a liquid to vaporize when subjected to high pressure, since gases take up more space than liquids Water, for example, boils at temps below 100 C up in the mountains where the air pressure is lower. (Water boils at 90 C at 10,000 ft.) It takes longer to cook food in boiling water at high altitudes because the boiling water isn't as hot. In a vacuum water will boil at any temp, since there is no pressure at the surface to prevent the water from vaporizing. At high pressure water boils at a high temp. In a pressure cooker water can remain liquid up to 120 C, and the hotter water can cook food faster.
Freezing of Solutions The freezing point of a solution, such as salt water, is lower than the freezing point for the solvent by itself, e.g., pure water. The higher the concentration of the solute, e.g. salt, the more the freezing point is lowered. The reason it is more difficult to freeze a liquid when a substance is dissolved in it is because the "foreign" molecules or atoms of a solute interfere with the molecules of the solvent as they're trying to form a crystalline structure. In the case of salt water, the sodium and chloride ions from the dissolved salt get in the wav and make it harder for the water molecules to crvstallize as a solid.
Boiling of Solutions If you're in a hurry and you need to bring water to boil on a stove, should you add salt to it? answer: No, salt actually increases the boiling point of water, thereby increasing your wait. In order for water to boil, the vapor pressure of the water must match to air pressure around it. The hotter the water, the higher the vapor pressure will be. Ion:s from the dissolved salt take up space near the surface of the water. With fewer water molecules exposed to the air, the vapor pressure is reduced. This means that salt water must be greater than 100 C in order to boil.
Pressure Depends on Depth, not Shape All these containers are the same height. Therefore, the pressure at the bottom of each is the same. The shape matters not! (See upcoming slides for further explanation.) Note: We're talking about the pressure inside the fluid, not the pressures exerted by the containers on the table, which would greater for a cylinder than a cone of the same height & base
Barometers The pressure at A is the same as the pressure of the surrounding air, since it's at the surface. A and B are at the same pressure, since they are at the same height. The pressure at C is zero, since a vacuum has no pressure. The pressure difference from B to C is gh (where is the density of mercury), which is the pressure at B, which is the pressure at A, which is the air pressure. Thus, the height of the barometer directly measures air pressure. At normal air pressure, h ~ 30 inches (760 mm), which is 760 torr. The weight of the column of mercury is balanced by the force exerted at the bottom due to the air pressure. Since mercury is 13.6 times heavier than water, a water barometer would have to be 13.6 times longer vacuum mercury
Hydraulic Press (cont.) The volume of oil pushed down on the left is the same as the increase on the right, so A h A2h2. Using the result on the last slide, we get: 2121111 This shows that the output work equals the input work (ideally) as conservation of energy demands. It's that force distance tradeoff again. With friction, the input work would be greater lo F. A2 oil
Archimedes' Principle Archimedes' principle states that any object that is partially or completely submerged in a fluid is buoyed up a force equal to the weight of the fluid that the object displaces. In the pic below, a hunk of iron, a chunk of wood, and a vacuum are all submerged. Since each is the same size, they all displace the same amount of fluid. Archimedes' principle says that the buoyant force on each is the weight of the fluid that would fit into this shape: iron wood For the iron, mg > FB (assuming iron is denser than the fluid), so it sinks. For the wood, mg < FB (assuming the fluid is denser than wood), so it floats to the surface. continued on next slide vacuum
Archimedes' Principle (cont.) Part of Captain Hook's boat is below the surface. Archimedes' principle says that the weight of the water Hook's boat displaces equals the buoyant force, which in this case is the weight of the boat and all on board, since the boat is floating. In the pic on the right, the boat is floating, so FB mboat g. Archimedes says FB mwg, the weight of water displaced by the boat (shaded). Thus, mwg mboat g, or m mboat This means the more people in the boat, the heavier it will be, and the lower the boat will ride. Barges adjust their height by taking on and pumping out water. Steel can float if shaped like a boat, because in that shape it can displace as much water as its own weight. boat
Bernoulli Equation: P2 constant Y2 ! y P = pressure v = fluid speed = fluid density (a constant) y = height As a nonviscous, incompressible fluid flows through a pipe that changes in both area and height, the pressure and fluid speed change, but the above expression remains constant everywhere in the pipe.
Bernoulli Equation Proof P2 X2 A y2 1 Fi Let green volume-purple volume = V. The volumes travel through the pipe in the same time. Let's look at the work done on all the fluid from A1 to A2 by the pressure in the pipe at each end as the fluid at the bottom moves a distance x continued on next slide
Bernoulli Equation Proof (cont.) The last equation shows that P + pv 2 + gy is the same before and after traveling from the left end of the pipe to the right end. Since these two places are completely arbitrary, our derivation shows that P+ 2 pv2+ pgy is a constant throughout the pipe, and the Bernoulli equation is proven! This equation is useful in many applications, from aviation to medicine.
Bernoulli Example 1 In an unfortunate mishap, the Tidy Bowl man gets flushed. With the info given below, let's figure out the pressure difference he and his boat experience as he travels across the pipe. Since the wider pipe has 4 times the area, the water speed there is 4 times slower (recall Av- constant). So, v2 = 2 m/s, which means P2 > Pl. From Bernoulli's equation at a constant height, we get: = ( 1000 kg / m3) (64 m2/s2-4 m2/s?) = 30 000 kg/(ms?) = 30000 kg m/(s2 m2) = 30000 N/(m2) = 30 000 Pa 8 m/s P2 4 A
Bernoulli Example 2 air flow wate Three vertical pipes open up inside the top pipe, in which air is flowing. Because air flows faster in the thin section of the top pipe, the pressure is lower there, and the water level beneath it rises more than in the other two. The difference in pressure between the thick section of the top pipe and the thin section is given by: ,gh.
Different kinds of fluids flow more easVisoosity l, for example, flows more easily than molasses. This is because molasses has a higher viscosity, which is a measure of resistance to fluid flow. Inside a pipe or tube a very thin layer of fluid right near the walls of the tube are motionless because they get caught up in the microscopic ridges of the tube. fastest The more viscous a fluid is, the more the layers want to cling together, and the more it resists this shearing. The resistance is due the frictional forces between the layers as the slides past one another. Note, there is no friction occurring at the tube's surface since the fluid there is essentially still. The friction happens in the fluid and generates heat. The Bernoulli equation applies to fluids with negligible viscosity.
Cohesion & Adhesion The force of attraction between unlike charges in the atoms or molecules of substances are responsible for cohesion and adhesion. Cohesion is the clinging together of molecules/atoms within a substance. Ever wonder why rain falls in drops rather than individual water molecules? It's because water molecules cling together to form drops. Adhesion is the clinging together of molecules/atoms of two different substances. Adhesive tape gets its name from the adhesion between the tape and other objects. Water molecules cling to many other materials besides clinging to themselves. continued
positive side HH Why molecules "cling" To understand why molecules cling to each other or to other molecules lets take a closer look at water. Each blue line represents a single covalent bond (one shared pair of electrons). Two other pairs of electrons also surround the central oxygen atom. The four electron pairs want to spread out as much as possible, which negative side gives H2O its bent shape. It is this shape that account for water's unusual property of expanding upon freezing The shared electrons are not shared equally. Oxygen is more electronegative than hydrogen, meaning this is an unequal tug-o-war, where the big, strong oxygen keeps the shared electrons closer to itself than to hydrogen. The unequal sharing, along with the electron pairs not involved in sharing, make water a polar molecule. Water is neutral, but it has a positive side and a negative side, This accounts for water's cohesive and adhesive nature as well as its ability to dissolve so many other substances
Why molecules "cling" (cont.) The dashed lines represent weak, temporary bonds between molecules. Water molecules can cling to other polar molecules besides them-selves, which is why water is a good solvent Water won't dissolve nonpolar molecules, like grease, though. (Detergent molecules have polar ends to attract water and nonpolar ends to mix with the grease.) Nonpolar molecules can attract each other to some extent, otherwise they couldn't exist in a liquid or solid state. This attraction is due to random asymmetries in the electron clouds around the nuclei of atoms