What are some properties of fluids? Why does a lake freeze from the top downward?

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1 Fluid Mechanics > A fluid is any substance that capable of flowing, which includes liquids, gases and powdered solids. Therefore fluids have some similar mechanical properties. ex; Both can not support shear stresses (unlike solids which can be elastically deformed). term liquid from Ltn. - to flow Two families of study within fluid mechanics; > hydrostatics ---> branch of mechanics concerned with the equilibrium of fluids > hydrokinematics ---> the study of fluid flow 1. density 2. buoyancy 3. pressure 4. viscosity 5. surface tension cohesion DENSITY What are some properties of fluids? >To say something is heavier or lighter are general terms, and the ambiguity can be removed by comparing equal volumes of substances. Thus, it is better to use the term density which expresses the compactness of matter in a specified volume. Density is a measure of the amount of matter contained in a specified volume. [Gk. pycnos -----> dense] *The density of a (uniform) material does not depend on size & shape! *The density maximum of most materials occurs in the solid state. [for H 2 O it is in the liquid C] *The density of a gas varies with temperature & pressure. Why does a lake freeze from the top downward? >Water is at its smallest volume (& highest density) at 3.98 C. [See two graphs!] As the water surface is cooled down to 3.98 C, this denser water sinks to the bottom. If all the water is cooled to 3.98 C it will become isothermal and all convective motion ceases. If the surface layer is cooled below 3.98 C, the surface layer will become less dense and remain on top. Eventually upon being cooled to 0 C, it solidifies. [1.0 ml of water cooled from 4 C to 0 C expands 9%, and its new (solid) volume = 1.09 ml] >Life would not exist if it were not for this unique property of water, as open bodies of water would freeze from the bottom upwards. ρ = 1.0 g/ml means that 1.0 ml weighs 1.0 g ρ = 2.0 g/ml means that 1.0 ml weighs 2.0 g ρ = 0.5 g/ml means that 1.0 ml weighs 0.5 g note! 1.0 g/cm3 = 1,000 kg/m3 earth crust ~ 2.7 g/cm 3 mantle ~ 4.7 g/cm 3 outer core ~ 11.0 g/cm 3 inner core ~12.5 g/cm 3

2 Given a gold ring as a gift, how would you know if it was pure gold? -Measure mass and volume, then compute the density and compare the value in a reference book. note! You must have that accepted value. [gold (Au) =19.3 g/cm3] How can the volume of an irregular-shaped object be calculated? Archimedes Gk. ( B.C.E.) of Syracuse, who was an advisor to King Hieron, was asked (~ 260 B.C.E.) to determine whether a goldsmith had cheated him by diluting a gold crown he had ordered with a metal of lesser value (silver). Since it was known that silver was lighter than gold, the smith could have added some extra silver to bring the weight up to the correct weight. The problem was how to measure the volume of an irregular object? While bathing in a private bath Archimedes notices the water which overflowed as he entered the full tub must be the volume of that part of him submerged (knowing he and the water could not occupy the same space at the same time). In other words; the volume of water displaced equals the volume of submerged body. Legend has it that he then ran through the streets of Syracuse naked yelling eureka... meaning I found it. By using the water displacement method, he reasoned that if the crown was pure gold, then it would displace the same amount of water as that of an equal weight of gold. But if the crown displaced a larger amount of water than an equal weight of gold (gold being denser would displace a smaller volume of water), then one could conclude that a metal of lesser density had been mixed with the gold by the smith. He solves the question by only getting the crown wet! How to calculate density? mass density ( ρ) expresses mass per unit volume: = m / V ( ρ) ----> rho ex; H 2 O (l) = 1.0 g/cm 3 or 1,000 kg/m 3.98 C [1 cm 3 = 1 cc = 1 ml] Hg = 13.6 g/cm 3, Pb = 11.3 g/cm 3, Au = 19.3 g/cm 3, Pt = 21.4 g/cm 3 ex; What would be the volume of 2 kg of copper (Cu) at 8,900 kg/m 3? sol; ρ cu = m / V -----> V = m / ρcu -----> = 2 kg / 8,900 kg /m 3 = 2.2 x 10-4 m 3 ex; Which has a larger volume; 15 kg of lead (Pb) or 10 kg of aluminum (Al)? sol; V Pb = m / ρ Pb -----> = 15 kg /11,400 kg/m 3 = 1.3 x 10-3 m 3 V Al = m / ρ Al -----> = 10 kg /2,700 kg/m 3 = 3.7 x 10-3 m 3 BUOYANCY How do objects float? Archimedes Principle: >If an object is placed in a fluid and floats, the weight of the displaced fluid will be equal to the weight of the object. >A floating body displaces its own weight of fluid in which it is floating in. >A floating body when placed in a liquid sinks until it displaces its own weight of liquid. >A body immersed wholly/partially in a fluid is buoyed up by a force equal to the wt. of the fluid displaced. >If the weight of the object (in air) is less than (or equal to) the water it displaces, it will float. >Any object immersed in a fluid appears to lose an amount of weight equal to that of the liquid it displaces. >An object will sink if its weight exceeds that of the weight of the displaced fluid.

3 buoyancy (B) or F b = the upward force that pushes objects up against gravity in a fluid = the weight of the fluid displaced [ex. s; lifting objects in pools, divingboard pull-ups] B = mg = ρvg = the weight of the fluid displaced >When the F b > weight of solid submerged in it, then the objects weight is not sufficient to keep it under the surface, and thus it will float. ex; A woman weighs 50 kg (50,000 g) displaces 45 kg of water. Will she float? sol; 50 kg > 45 kg, and she will not float. ex; A cube 0.2 m on each side has a mass of 7.2 kg. Will this cube float in water? sol; ρ c = m / V -----> 7.2 kg / m 3 = 900 kg/m 3 < ρ w =1,000 kg/m 3 Cube will float. ex; A 200 cm 3 block of aluminum weighs 340 g when immersed in water. What is its weight in air? sol; 200 cm 3 of water will be displaced, which weighs 200 g. (B) acting up on the block is 200 g of force. Thus, out of water, scale will read 540 g. ex; A cube 1.0 m on each side is held completely submerged under water. What force is required to do this? [hint: You must apply a force equal and opposite to the buoyant force.] sol; B = ρvg = weight of water displaced. V = 1.0 m 3 & density of displaced water ( ρw) = 1,000 kg/m 3 B = (1,000 kg/m 3 )(1.0 m 3 )(9.8 m/s 2 ) = 9,800 N (That is a lot of force! About four adult males would need to stand atop of the box to accomplish this.) Most metals float on Hg. Rocks do not float because the mass of water displaced is less less than the mass of the rock! Concrete boat? Yes, they exist. Who sinks? >Dense muscle-bound people (football players) are more likely to sink, whereas people with much body fat are more likely to float. >Most adults need an extra 7-12 lb of buoyancy to keep their heads above water long-term. >Body fat, lung size, clothing, calmness of person all play a part in staying afloat. >Generally, the more physically fit one is, the more lift will be needed. >By body immersion in water, the % of fat on athletes can be calculated. -Weigh person in air, then in water; this difference indicates the density of the body. How do metal ships float? > Actually, the overall density of a steel ship is less than that of water because the interior is hollow and largely empty. [First concept of building ships of iron was ridiculed!] > The total weight of a ship is called its displacement, which equals the weight of the water displaced. Thus, if a body is capable of floating, then (B) = the whole weight of the body. > A 10,000-ton ship must be designed wide enough to displace 10,000 tons of water before it sinks too deep into the water. [Note that ships float higher in denser salt water.]

4 ex; A newly constructed ship has a total weight of 1,472,000 lb and is launched into seawater. What volume of seawater will be displaced after it has been launched? sol; D = W / V -----> V = W / D = 1,472,000 lb / 64 lb/ft 3 = 23,000 ft 3 ex; The RMS Titanic displaced approximately 1,830,850 ft 3 of seawater. Knowing this displacement, what was the weight of this ship? sol; D = W / V -----> W = DV = (64 lb/ft 3 )(1,830,850 ft 3 ) = 117,174,400 lb >Submarines submerge and surface because of buoyancy. *When the ballast tanks are flooded with seawater, the average density of the vessel is > seawater -----> sink. *When the ballast tanks are pumped out, the average density of the vessel is < seawater -----> rise. *Merchant ships would load and unload ballast stones when trading. [discuss Belgian blocks used as pavers] How do balloons float in air? All balloons float because the weight of the displaced air weighs more that the balloon. >For hot air ballons; - The heated air expands, and the large volume of air displaced actually weighs more than the balloon. - A 5-ton hot air balloon must displace at least 5 tons of air. ex; Compute the buoyant force (B) on a balloon containing 1,600 m 3 of helium. [density of air = 1.29 kg/m 3 ] sol; Weight of air displaced? -----> W air = B = ρvg = (1.29 kg/m 3 )(1,600 m 3 )(9.8 m/s 2 ) = 20,227 N ex; What is the lifting force of the Hindenburg airship which displaced 7,062,100 ft 3 of air. [D air = lb/ft 3 ] sol; Weight of air displaced? -----> D = W / V -----> W = DV = (0.081 lb/ft 3 )(7,062,100 ft 3 ) = 572,030 lb When one totals the weight of the airship, 4 diesel engines, fuel, cargo, mail, passengers, crew and luggage it equalled about 470,000 lb. ex; Why do objects weighed in air and in a vacuum have differing weights? sol; An object in a vacuum displaces no fluid, so there is no upward buoyancy force and will weigh more. Historical: - On Sept.19, 1783 Fr. Joseph and Etienne Montgolfier using a hot-air balloon sent a duck, rooster, and a lamb up to a height of 500 meters for 8 minutes. - On Oct.15, 1783 the first human flight was by the Montgolfier brothers in a 20 m tethered hot-air balloon. - On Oct.19th they reached about 100 m, and on Oct. 21st it reached about 350 m, flying 9 km in 20 minutes. - On Dec.1st Fr. Jacques Charles fills a balloon with hydrogen by pouring H 2 SO 4 onto a pile of iron filings. His Charliere rose to 1,000 m! [The Montgolfier brothers were the first to try (H 2 ) but the gas quickly escaped.]

5 Hydrometers: > The depth to which a floating body immerses itself in a liquid can be used to measure a liquid s density. > A floating body displaces a weight of liquid equal to its own weight. Hence, the lighter (less dense) the liquid, the greater the depth to which the hydrometer will sink in it. - Hydrometers are used to measure the specific gravity of milk, ethanol, battery acid, and auto radiator fluid.