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# Fluid mechanics 1

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### Fluid mechanics 1

1. 1. Fluid MechanicsFluid MechanicsChapter 8Chapter 8
2. 2. Fluids and BuoyantFluids and BuoyantForceForceSection 1Section 1
3. 3. Defining a FluidDefining a FluidAA fluidfluid is a nonsolid state of matter in which theis a nonsolid state of matter in which theatoms or molecules are free to move past eachatoms or molecules are free to move past eachother, as in a gas or a liquid.other, as in a gas or a liquid.Both liquids and gases are considered fluidsBoth liquids and gases are considered fluidsbecause they can flow and change shape.because they can flow and change shape.Liquids have a definite volume; gases do not.Liquids have a definite volume; gases do not.
4. 4. Density and Buoyant ForceDensity and Buoyant ForceThe concentration of matter of an object isThe concentration of matter of an object iscalled thecalled the mass densitymass density..Mass density is measured as the mass perMass density is measured as the mass perunit volume of a substance.unit volume of a substance.ρ =mVmass density =massvolume
5. 5. Densities of Common SubstancesDensities of Common Substances
6. 6. Density and Buoyant ForceDensity and Buoyant ForceTheThe buoyant forcebuoyant force is the upward forceis the upward forceexerted by a liquid on an object immersedexerted by a liquid on an object immersedin or floating on the liquid.in or floating on the liquid.Buoyant forces can keep objects afloat.Buoyant forces can keep objects afloat.
7. 7. Buoyant Force and ArchimedesBuoyant Force and Archimedes’’PrinciplePrincipleThe Brick, when added will cause the water toThe Brick, when added will cause the water tobe displaced and fill the smaller container.be displaced and fill the smaller container.What will the volume be inside the smallerWhat will the volume be inside the smallercontainer?container?The same volume as the brick!The same volume as the brick!
8. 8. Buoyant Force and ArchimedesBuoyant Force and Archimedes’’PrinciplePrincipleArchimedesArchimedes’’ principle describes the magnitudeprinciple describes the magnitudeof a buoyant force.of a buoyant force.ArchimedesArchimedes’’ principle:principle: Any object completely orAny object completely orpartially submerged in a fluid experiences anpartially submerged in a fluid experiences anupward buoyant force equal in magnitude to theupward buoyant force equal in magnitude to theweight of the fluid displaced by the object.weight of the fluid displaced by the object.FFBB == FFgg (displaced fluid)(displaced fluid) == mmffggmagnitude of buoyant force = weight of fluid displacedmagnitude of buoyant force = weight of fluid displaced
9. 9. Buoyant ForceBuoyant ForceThe raft and cargoThe raft and cargoare floatingare floatingbecause theirbecause theirweight andweight andbuoyant force arebuoyant force arebalanced.balanced.
10. 10. Buoyant ForceBuoyant ForceNow imagine a small holeNow imagine a small holeis put in the raft.is put in the raft.The raft and cargo sinkThe raft and cargo sinkbecause their density isbecause their density isgreater than the density ofgreater than the density ofthe water.the water.As the volume of the raftAs the volume of the raftdecreases, the volume ofdecreases, the volume ofthe water displaced by thethe water displaced by theraft and cargo alsoraft and cargo alsodecreases, as does thedecreases, as does themagnitude of the buoyantmagnitude of the buoyantforce.force.
11. 11. Buoyant ForceBuoyant ForceFor a floating object, the buoyant force equals theFor a floating object, the buoyant force equals theobjectobject’’s weight.s weight.The apparent weight of a submerged objectThe apparent weight of a submerged objectdepends on the density of the object.depends on the density of the object.For an object with densityFor an object with density ρρOO submerged in a fluidsubmerged in a fluidof densityof density ρρff, the buoyant force, the buoyant force FFBB obeys theobeys thefollowing ratio:following ratio:Fg(object)FB=ρOρf
12. 12. ExampleExampleA bargain hunter purchasesA bargain hunter purchasesaa ““goldgold”” crown at a fleacrown at a fleamarket. After she getsmarket. After she getshome, she hangs the crownhome, she hangs the crownfrom a scale and finds itsfrom a scale and finds itsweight to be 7.84 N. Sheweight to be 7.84 N. Shethen weighs the crown whilethen weighs the crown whileit is immersed in water, andit is immersed in water, andthe scale reads 6.86 N. Isthe scale reads 6.86 N. Isthe crown made of purethe crown made of puregold? Explain.gold? Explain.
13. 13. SolutionSolutionρρ==– apparent weightg Bg OB fF FFF( )ρ ρ==– apparent weightB ggO fBF FFFChoose your equations:Choose your equations:Rearrange your equations:Rearrange your equations:
14. 14. SolutionSolutionPlug and Chug:Plug and Chug:From the table in your book, the densityFrom the table in your book, the densityof gold is 19.3of gold is 19.3 ×× 101033kg/mkg/m33..Because 8.0Because 8.0 ×× 101033kg/mkg/m33< 19.3< 19.3 ×× 101033kg/mkg/m33, the crown cannot be pure gold., the crown cannot be pure gold.( )ρ ρρ== = ×= ×3 33 37.84 N – 6.86 N = 0.98 N7.84 N1.00 10 kg/m0.98 N8.0 10 kg/mBgO fBOFFF
15. 15. Your Turn IYour Turn IA piece of metal weighs 50.0 N in air and 36.0 NA piece of metal weighs 50.0 N in air and 36.0 Nin water and 41.0 N in an unknown liquid. Findin water and 41.0 N in an unknown liquid. Findthe densities of the following:the densities of the following:The metalThe metalThe unknown liquidThe unknown liquidA 2.8 kg rectangular air mattress is 2.00 m longA 2.8 kg rectangular air mattress is 2.00 m longand 0.500 m wide and 0.100 m thick. Whatand 0.500 m wide and 0.100 m thick. Whatmass can it support in water before sinking?mass can it support in water before sinking?A ferry boat is 4.0 m wide and 6.0 m long. WhenA ferry boat is 4.0 m wide and 6.0 m long. Whena truck pulls onto it, the boat sinks 4.00 cm in thea truck pulls onto it, the boat sinks 4.00 cm in thewater. What is the weight of the truck?water. What is the weight of the truck?
16. 16. PNBWPNBWPage 279Page 279Physics 1Physics 1--44Honors 1Honors 1--55
17. 17. Fluid PressureFluid PressureSection 2Section 2
18. 18. PressurePressureDeep sea divers wear atmospheric divingDeep sea divers wear atmospheric divingsuits to resist the forces exerted by thesuits to resist the forces exerted by thewater in the depths of the ocean.water in the depths of the ocean.You experience this pressure when youYou experience this pressure when youdive to the bottom of a pool, drive up adive to the bottom of a pool, drive up amountain, or fly in a plane.mountain, or fly in a plane.
19. 19. PressurePressurePressurePressure is the magnitude of the force on ais the magnitude of the force on asurface per unit area.surface per unit area.PascalPascal’’s principle states that pressure applied tos principle states that pressure applied toa fluid in a closed container is transmitteda fluid in a closed container is transmittedequally to every point of the fluid and to theequally to every point of the fluid and to thewalls of the container.walls of the container.P =FApressure =forcearea
20. 20. PressurePressureThe SI unit for pressure is theThe SI unit for pressure is the pascalpascal, Pa., Pa.It is equal to 1 N/mIt is equal to 1 N/m22..The pressure at sea level is about 1.01 xThe pressure at sea level is about 1.01 x101055Pa.Pa.This gives us another unit for pressure, theThis gives us another unit for pressure, theatmosphere, where 1atmosphere, where 1 atmatm = 1.01 x 10= 1.01 x 1055PaPa
21. 21. PascalPascal’’s Principles PrincipleWhen you pump a bike tire, you applyWhen you pump a bike tire, you applyforce on the pump that in turn exerts aforce on the pump that in turn exerts aforce on the air inside the tire.force on the air inside the tire.The air responds by pushing not only onThe air responds by pushing not only onthe pump but also against the walls of thethe pump but also against the walls of thetire.tire.As a result, the pressure increases by anAs a result, the pressure increases by anequal amount throughout the tire.equal amount throughout the tire.
22. 22. PascalPascal’’s Principles PrincipleA hydraulic lift usesA hydraulic lift usesPascals principle.Pascals principle.A small force is appliedA small force is applied(F(F11) to a small piston of) to a small piston ofarea (Aarea (A11) and cause a) and cause apressure increase on thepressure increase on thefluid.fluid.This increase in pressureThis increase in pressure((PPincinc) is transmitted to the) is transmitted to thelarger piston of area (Alarger piston of area (A22))and the fluid exerts aand the fluid exerts aforce (Fforce (F22) on this piston.) on this piston.F1F2A1A22211AFAFPinc ==1212AAFF =
23. 23. ExampleExampleThe small piston of a hydraulic lift has anThe small piston of a hydraulic lift has anarea of 0.20 marea of 0.20 m22. A car weighing 1.20 x 10. A car weighing 1.20 x 1044N sits on a rack mounted on the largeN sits on a rack mounted on the largepiston. The large piston has an area ofpiston. The large piston has an area of0.90 m0.90 m22. How much force must be applied. How much force must be appliedto the small piston to support the car?to the small piston to support the car?
24. 24. SolutionSolutionPlug and Chug:Plug and Chug:FF11 = (1.20 x 10= (1.20 x 1044N) (0.20 mN) (0.20 m22/ 0.90 m/ 0.90 m22))FF11 = 2.7 x 10= 2.7 x 1033NN2211AFAF=2121AAFF =
25. 25. Your Turn IIYour Turn IIIn a car lift, compressed air exerts a force on aIn a car lift, compressed air exerts a force on apiston with a radius of 5.00 cm. This pressure ispiston with a radius of 5.00 cm. This pressure istransmitted to a second piston with a radius oftransmitted to a second piston with a radius of15.0 cm.15.0 cm.How large of a force must the air exert to lift a 1.33 xHow large of a force must the air exert to lift a 1.33 x101044 N car?N car?A person rides up a lift to a mountain top, but theA person rides up a lift to a mountain top, but thepersonperson’’s ears fail tos ears fail to ““poppop””. The radius of each. The radius of eachear drum is 0.40 cm. The pressure of theear drum is 0.40 cm. The pressure of theatmosphere drops from 10.10 x 10atmosphere drops from 10.10 x 1055 Pa at thePa at thebottom to 0.998 x 10bottom to 0.998 x 1055 Pa at the top.Pa at the top.What is the pressure difference between the inner andWhat is the pressure difference between the inner andouter ear at the top of the mountain?outer ear at the top of the mountain?What is the magnitude of the net force on eachWhat is the magnitude of the net force on eacheardrum?eardrum?
26. 26. PressurePressurePressure varies with depth in a fluid.Pressure varies with depth in a fluid.The pressure in a fluid increases withThe pressure in a fluid increases withdepth.depth.( )ρ= +× ×0absolute pressure =atmospheric pressure +density free-fall acceleration depthP P gh
27. 27. PNBWPNBWPage 283Page 283Physics 1Physics 1--33Honors 1Honors 1--44
28. 28. Fluids in MotionFluids in MotionSection 3Section 3
29. 29. Fluid FlowFluid FlowMoving fluids can exhibitMoving fluids can exhibit laminarlaminar (smooth)(smooth)flow orflow or turbulentturbulent (irregular) flow.(irregular) flow.LaminarFlow Turbulent Flow
30. 30. Fluid FlowFluid FlowAnAn ideal fluidideal fluid is a fluid that has no internalis a fluid that has no internalfriction or viscosity and is incompressible.friction or viscosity and is incompressible.The ideal fluid model simplifies fluidThe ideal fluid model simplifies fluid--flowflowanalysisanalysis
31. 31. Fluid FlowFluid FlowNo real fluid has all the properties of anNo real fluid has all the properties of anideal fluid, it helps to explain the propertiesideal fluid, it helps to explain the propertiesof real fluids.of real fluids.Viscosity refers to the amount of internalViscosity refers to the amount of internalfriction within a fluid. High viscosity equalsfriction within a fluid. High viscosity equalsa slow flow.a slow flow.Steady flow is when the pressure,Steady flow is when the pressure,viscosity, and density at each point in theviscosity, and density at each point in thefluid are constant.fluid are constant.
32. 32. Principles of Fluid FlowPrinciples of Fluid FlowThe continuity equation results fromThe continuity equation results fromconservation of mass.conservation of mass.Continuity equation:Continuity equation:AA11vv11 == AA22vv22AreaArea ×× speed in region 1 = areaspeed in region 1 = area ×× speed in region 2speed in region 2
33. 33. Principles of Fluid FlowPrinciples of Fluid FlowThe speed of fluid flowThe speed of fluid flowdepends on crossdepends on cross--sectional area.sectional area.BernoulliBernoulli’’s principles principlestates that the pressurestates that the pressurein a fluid decreases asin a fluid decreases asthe fluidthe fluid’’s velocitys velocityincreases.increases.
34. 34. PNBWPNBWPage 286Page 286Physics 1Physics 1--33Honors 1Honors 1--44