Buoyancy Archimedes Principle Fluid Flow Viscosity
Lecture 8BuoyancyArchimedes PrincipleFluid flowViscosity
Buoyancy and Archimedes PrincipleOne’s body ,arms and legs etc, feel lighter under water.Easy to lift someone if they are in a swimming pool.Archimedes principle:Any object completely or partially immersedin a fluid experiences an upward or buoyantforce equal to the weight of the fluid it displaces.Archimedes (287 BC – 212 BC)Greek Physicist, MathematicianBuoyant force easily explainedPressure is greater atgreater depth: P rghtherefore the upward force isgreater at the bottom of anobject than the downwardforce at the top of the objectF1F2F2 F1Net upward force is the buoyant forceis equal to the weight of the displaced fluid.
Buoyancy and Archimedes PrincipleCube of same fluidh1P1A1h2mgP1 rgh1P2 rgh2P2A2Buoyant force FbFb P2A2- P1A1Cube remains stationaryFb weight of fluid weight of fluiddisplacedFb P2A2- P1A1 mfgwhere mf mass of fluidCube of different material (only mass of cubechanges) buoyant force remains unchanged(Fb mfg)Fb mfg rfluidVfluidg If an object floats then the buoyant forcemust equal its weight. If an object sinks then its weight must begreater than the buoyant force.
Buoyancy and Archimedes Principle00wobject - FbwobjectFluidApparent weight net downward force wobject - FbFb weight – apparent weightFb weight of liquid displaced
Buoyancy and Archimedes PrincipleCalculate the volume and density of anIrregular shaped object.ExampleA person has a mass of 75kg in air and anapparent mass of 2kg when submerged in water.Calculate the volume and density of the person.Fb weight – apparent weightmass of water displaced Mass – apparent massmass of water displaced 75kg – 2kg 73kgVolume of water displaced (mwater)/(rwater) 73kg/1000kgm-3 73x10-3m3Therefore volume of person 73x10-3m3rperson (mperson)/(volumeperson)rperson (75kg)/(73x10-3m3) 1027kgm-3
Viscosity and Fluid flowOne characteristic of fluids is that they flowFluid flow in tubes:examples: IV tubes, garden hoses, circulatory systemFlow rate Q defined as volume flowingper unit time (V/t)Q (V/t)SI units: m3 per secondFlow rate depends on pressure difference other characteristics of the fluid and tube
Viscosity and Fluid flowQ (V/t)Flow rate depends on pressure differenceP1P1 P2 no flowP2LP1 P2 flow directionP1 P2 flow directionP1 P2Flow rate Q Rwhere R is the resistance to flow.Resistance is all factors that impair flow; example, friction between fluid and tube, friction within the fluid** known viscosity h(Greek letter eta).SI unit of viscosity N.s.m-2
Viscosity and Fluid flowFlow can be characterised as laminar turbulentTurbulent flowFluctuating flow patternsCaused by constrictions or obstructionsTurbulence causes increased resistance to flow
Viscosity and Fluid flowLaminar flowSmooth, streamlined, quietResistance to laminar flow of an incompressiblefluid in a tube is a function of8h L tube length (L),R 4 radius (r) r viscosity h1R 4rdouble radius; resistancedecreases by a factor of 16
Viscosity and Fluid flow8h LR 4 rP1 P2Flow rate Q R r4 Q ( P1 P2 8h L Poiseuille’s LawFrench scientist Jean Poiseuille (1797-1869)studied fluid flow in tubes; in particular blood flow
Viscosity and Fluid flowFluid flowTeethSensitivity to cold, heat, air,Concerned with fluid flowwithin the toothFluid flowdentinal tubules (microscopic channels)radiate outward through the dentine fromthe pulp to the dentine-enamel interface.If outer enamel develops a crack or cavitywhen you eat cold food, for examplenormal fluid flow within the dentine may bedisrupted – affecting the pulp (nerves , bloodvessels etc), resulting in pain.
Viscosity and Fluid flowTo change flow rate; change radius of tubeExamples Blood flow rate in circulatory system changedby constricting or dilating blood vessels Clamp on IV tubing Tap on garden hoseFlow rate Q r4 Q ( P1 P2 8h L Q r4If effective radius of a vein or artery is reducedby a constriction (deposits) blood circulation problems occur.Result: heart has to work considerably harder toproduce a higher blood pressure in order tomaintain the required flow rate.
ViscosityMaterialsResistance to fluid flowDentistryRestorative materials are manipulated in fluidstate to achieve desired resultViscosity of cement should be low so that itwill flow over tooth surface to achieve goodretentionMaterials Prepared as fluid pastes adapted to the required shape subsequently solidifySetting of such materialsChange of viscosity with time
ViscosityRestorative Dental MaterialInitial low viscosity for dispensing andmoulding.Followed by large increase in viscosityduring settingWorking time – time during which the materialcan be easily manipulated (low viscosity)Setting time – time at which viscositybecomes very highTimeNo well definedworking time orsetting timeViscosityViscosityViscosityChange of material viscosity with timeTimeTimeWell defined longLong working timeworking time andreasonablesudden setting time setting time
Viscosity and Fluid flowExampleIf effective radius of the artery is halved, bywhat factor does the blood flow rate change? r4 Q0 ( P1 P2 8h L r 4 2Q ( P1 P2 8h L Q11 4 Q0 2 16Q0Q 16Factor of 16
Viscosity and Fluid flowExampleBy what percentage would the radius of thearteries have to decrease to reduce the bloodflow rate by a factor of 3. r4 Q0 ( P1 P2 8h L Q0 rn4 ( P1 P2 3 8h L Dividing the two equationsQ0 r ( P1 P2 3 8h L 4n r4 Q0 ( P1 P2 8h L 1 rn4 43 rr14 n 0.763 rrn 0.76rReduction of (1-0.76)x100% 24%
Viscosity and Fluid flowExamplePatient receiving blood transfusion through a needleof length 2.3cm and radius 0.2mm. The reservoirsupplying the blood is 0.7m above the patients arm.Determine the flow rate through the needle.Density of blood is 1050kgm-3. Viscosity of blood is2.7x10-3N.s.m-2Pressure difference P1-P2 rghP1 – P2 (1050kgm-3)(9.8ms-2)(0.7m) 7.20 x103Pa. r4 Q ( P1 P2 8h L (2 10 4 m)43Q 7.20 10Pa ( -3-2 2 8(2.7 10 Nsm ) 2.3 10 m Q 7.28 x 10-8m3s-1
Viscosity and Fluid flowFlow rate and pressure dropP1 P2Q RP1 P2 QRWater mainP1Water supplyto homesP2If P1 P2 no flowIf many users draw water simultaneouslylarge flowlarge pressure dropHence P2 is smaller than when usage is light.Solutions: increase P1 and/ordecrease R (increase diameter of water main)Both occur during vigorous exercisein the circulatory systemBlood pressure increases and arteries dilate
Buoyancy and Archimedes PrincipleObjects that floatObject’s weight is equal to the buoyant force Fbwobject FbApplying Archimedes principleFb is equal to weight of fluid displacedthereforewobject wfluid (displaced)True only if object floatsFb mfg rfluidVfluidg Fb mfg robjectVobjectgrfluidVfluidg robjectVobjectgrobject Vfluidrfluid Vobjectvolume of object submerged volume of fluid displaced“The fraction of the object that is submerged isequal to the ratio of the density of the objectto the density of the fluid.”
Buoyancy and Archimedes PrincipleApplicationsWhy do ships floatAverage density is less than that of waterShip partially submerges until weight of shipequals weight of water displaced.Hot air (or Helium) balloonsHot air less dense that cold air resulting in anet upward force on the balloonsHuman brain is immersed in cerebrospinal fluid,density 1007 kgm-3average density of brain 1040 kgm-3Most of brain’s weight is supported bythe buoyant force
Buoyancy and Archimedes PrincipleObjects that sink (totally submerged)Applying Archimedes principleFb is equal to weight of fluid displacedFb mfluidg (Vfluid)(rfluid)gBut volume of fluid displaced volume of objectthereforeFb (Vobject)(rfluid)gDownward gravitational force on objectmobjectg (robject) (Vobject)gNet force upwards on object Fb - wobject (Vobject)(rfluid)g -(robject) (Vobject)gNet force upwards (rfluid-robject)(Vobject)gIf rfluid robjectobject will floatIf rfluid robjectobject will sink
Buoyancy and Archimedes PrincipleCalculate the fraction of an iceberg’s volume that issubmerged when it floats in water. Density of ice 917kgm-3Fb rfluidVfluidgWeight of object (w) robjectVobjectgw Fbwiceberg wwatermiceberg mwaterVwater volume of water displacedriceberg mwater ricebergVwater Vicebergr water miceberg r waterriceberg Vwater917kgm 3 0.917 3r water Viceberg 1000kgm
Buoyancy and Archimedes PrincipleExampleDetermine the density of a liquid if an object ofknown volume (50cm3) and mass (0.150kg)has an apparent mass of 0.105kg in the liquid.Applying Archimedes principleBuoyant force is equal to weight of liquid displacedWeight – apparent weight weight of liquid displacedMass – apparent mass mass of liquid displaced0.150kg - 0.105kg 0.045kg is displaced by the objectVolume of object 50cm3 50x10-6m3 Volume of liquid displacedTherefore density of liquid (0.045kg) /(50x10-6m3) 900kgm-3
Buoyancy and Archimedes PrincipleA 70 kg statue lies at the bottom of the sea(Density 1.025x103 kg m-3). Its volume is3.0x104cm3. How much force do you needto lift it?Weight - Apparent weight weight of fluid displacedmg –Wapp weight of fluid displacedWapp mg –mfluid gWapp mg –rfluidVgWapp g(m –rfluidV)Wapp 9.8ms-2(70kg –1.025x103 kg m-3 3.0x10-2m3)Wapp 9.8ms-2( 70kg –30.75kg)384.65N
Buoyancy and Archimedes PrincipleYou immerse an object in water and measurethe apparent weight. You then repeat theprocess in salt solution (density slightlyhigher than water) would you expect thenew apparent weight to bea) Higherb) Samec) LowerApplying Archimedes principleFb is equal to weight of fluid displacedFb is equal to mg of fluid displacedFb is equal to rVg of fluid displaced
Buoyancy and Archimedes PrincipleA small car ferry measures 4.00 metres wide by6.00metres long. When several cars of total weight9.41 x103N drive on to it, it sinks an additionaldepth (d) into the water. Calculate the additional depth.Density of water 1000kgm-3It floats, therefore:object’s weight is equal to the buoyant force FbApplying Archimedes principleWobject FbFb is equal to weight of fluid displacedwobject wfluidAdditional volume (V) of ferry below water lineV 4m x 6m x dAdditional mass of ferry density x VolumeAdditional weight of ferry density x Volume x g4m x 6m x d x (1000kgm-3) x (9.8ms-2) 9.41kNd 4cm
A person has a mass of 75kg in air and an apparent mass of 2kg when submerged in water. Calculate the volume and density of the person. mass of water displaced Mass – apparent mass mass of water displaced 75kg – 2kg 73kg Volume of water displaced (m water)/(r water) 73kg/1000kgm
defined the buoyancy principle. Apparently (while in his bath) Archimedes realized that submerged objects always displace fluid upward (water in the bath rose while he was submerged). Then with that observation, he concluded that this force (buoyant) must be equal to the weight of the displaced fluid. Archimedes then went on to state that a
Activity 1: Buoyancy - Floating and Sinking Introduction An object or vessel floats when the weight of the water it displaces is equal to the weight of the object. This is known as Archimedes' principle. When an object has positive buoyancy, it is floating on the surface. To sink, the object needs to have negative buoyancy.
244LD Intelligent Buoyancy Transmitter with Torque Tube and Displacer for Level, Interface and Density - All versions - These intelligent transmitters are designed to perform measurements for liquid level, interface or density of liquids. The measurement is based on the Archimedes buoyancy principle. Easy remote configuration and supervision with
144LD Intelligent Buoyancy Transmitter with Torque Tube and Displacer for Level, Interface and Density with Communication HART / FoxCom These intelligent transmitters are designed to perform measurements for liquid level, interface or density of liquids. The measurement is based on the Archimedes buoyancy principle.
Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and Bernoulli's Equation 7. General Energy Equation 8. Reynolds Number, Laminar Flow, Turbulent Flow and Energy Losses Due to Friction
Buoyancy Buoyancy The ability of a fluid to exert an upward force on an object . objects in water, and helps to explain floating and sinking, and why objects seem lighter in water. It also applies to balloons in the air. . Buoyancy Author: Tecumseh High School
buoyancy coefficient for total tax revenue is usually high. high buoyancy coefficients may be masking weaknesses in the non-oil tax system. 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 1960-1965 1965-1970 1970-1974 tax buoyancy direct avg. crude oil 0.00 1.00 2.00 3.00 4.00 5.00 6.00
L M A B CVT Revision: December 2006 2007 Sentra CVT FLUID PFP:KLE50 Checking CVT Fluid UCS005XN FLUID LEVEL CHECK Fluid level should be checked with the fluid warmed up to 50 to 80 C (122 to 176 F). 1. Check for fluid leakage. 2. With the engine warmed up, drive the vehicle to warm up the CVT fluid. When ambient temperature is 20 C (68 F .
