Fluid mechanics 1
- 1. Fluid MechanicsFluid Mechanics Chapter 8Chapter 8
- 2. Fluids and BuoyantFluids and Buoyant ForceForce Section 1Section 1
- 3. Defining a FluidDefining a Fluid AA fluidfluid is a nonsolid state of matter in which theis a nonsolid state of matter in which the atoms or molecules are free to move past eachatoms or molecules are free to move past each other, 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 fluids because 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. Density and Buoyant ForceDensity and Buoyant Force The concentration of matter of an object isThe concentration of matter of an object is called thecalled the mass densitymass density.. Mass density is measured as the mass perMass density is measured as the mass per unit volume of a substance.unit volume of a substance. ρ = m V mass density = mass volume
- 5. Densities of Common SubstancesDensities of Common Substances
- 6. Density and Buoyant ForceDensity and Buoyant Force TheThe buoyant forcebuoyant force is the upward forceis the upward force exerted by a liquid on an object immersedexerted by a liquid on an object immersed in or floating on the liquid.in or floating on the liquid. Buoyant forces can keep objects afloat.Buoyant forces can keep objects afloat.
- 7. Buoyant Force and ArchimedesBuoyant Force and Archimedes’’ PrinciplePrinciple The Brick, when added will cause the water toThe Brick, when added will cause the water to be 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 smaller container?container? The same volume as the brick!The same volume as the brick!
- 8. Buoyant Force and ArchimedesBuoyant Force and Archimedes’’ PrinciplePrinciple ArchimedesArchimedes’’ principle describes the magnitudeprinciple describes the magnitude of a buoyant force.of a buoyant force. ArchimedesArchimedes’’ principle:principle: Any object completely orAny object completely or partially submerged in a fluid experiences anpartially submerged in a fluid experiences an upward buoyant force equal in magnitude to theupward buoyant force equal in magnitude to the weight of the fluid displaced by the object.weight of the fluid displaced by the object. FFBB == FFgg (displaced fluid)(displaced fluid) == mmffgg magnitude of buoyant force = weight of fluid displacedmagnitude of buoyant force = weight of fluid displaced
- 9. Buoyant ForceBuoyant Force The raft and cargoThe raft and cargo are floatingare floating because theirbecause their weight andweight and buoyant force arebuoyant force are balanced.balanced.
- 10. Buoyant ForceBuoyant Force Now imagine a small holeNow imagine a small hole is put in the raft.is put in the raft. The raft and cargo sinkThe raft and cargo sink because their density isbecause their density is greater than the density ofgreater than the density of the water.the water. As the volume of the raftAs the volume of the raft decreases, the volume ofdecreases, the volume of the water displaced by thethe water displaced by the raft and cargo alsoraft and cargo also decreases, as does thedecreases, as does the magnitude of the buoyantmagnitude of the buoyant force.force.
- 11. Buoyant ForceBuoyant Force For a floating object, the buoyant force equals theFor a floating object, the buoyant force equals the objectobject’’s weight.s weight. The apparent weight of a submerged objectThe apparent weight of a submerged object depends 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 fluid of densityof density ρρff, the buoyant force, the buoyant force FFBB obeys theobeys the following ratio:following ratio: Fg (object) FB = ρO ρf
- 12. ExampleExample A bargain hunter purchasesA bargain hunter purchases aa ““goldgold”” crown at a fleacrown at a flea market. After she getsmarket. After she gets home, she hangs the crownhome, she hangs the crown from a scale and finds itsfrom a scale and finds its weight to be 7.84 N. Sheweight to be 7.84 N. She then weighs the crown whilethen weighs the crown while it is immersed in water, andit is immersed in water, and the scale reads 6.86 N. Isthe scale reads 6.86 N. Is the crown made of purethe crown made of pure gold? Explain.gold? Explain.
- 13. SolutionSolution ρ ρ = = – apparent weightg B g O B f F F F F ( ) ρ ρ = = – apparent weightB g g O f B F F F F Choose your equations:Choose your equations: Rearrange your equations:Rearrange your equations:
- 14. SolutionSolution Plug and Chug:Plug and Chug: From the table in your book, the densityFrom the table in your book, the density of gold is 19.3of gold is 19.3 ×× 101033 kg/mkg/m33 .. Because 8.0Because 8.0 ×× 101033 kg/mkg/m33 < 19.3< 19.3 ×× 101033 kg/mkg/m33 , the crown cannot be pure gold., the crown cannot be pure gold. ( )ρ ρ ρ = = = × = × 3 3 3 3 7.84 N – 6.86 N = 0.98 N 7.84 N 1.00 10 kg/m 0.98 N 8.0 10 kg/m B g O f B O F F F
- 15. Your Turn IYour Turn I A 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 N in water and 41.0 N in an unknown liquid. Findin water and 41.0 N in an unknown liquid. Find the densities of the following:the densities of the following: The metalThe metal The unknown liquidThe unknown liquid A 2.8 kg rectangular air mattress is 2.00 m longA 2.8 kg rectangular air mattress is 2.00 m long and 0.500 m wide and 0.100 m thick. Whatand 0.500 m wide and 0.100 m thick. What mass 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. When a truck pulls onto it, the boat sinks 4.00 cm in thea truck pulls onto it, the boat sinks 4.00 cm in the water. What is the weight of the truck?water. What is the weight of the truck?
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- 17. Fluid PressureFluid Pressure Section 2Section 2
- 18. PressurePressure Deep sea divers wear atmospheric divingDeep sea divers wear atmospheric diving suits to resist the forces exerted by thesuits to resist the forces exerted by the water in the depths of the ocean.water in the depths of the ocean. You experience this pressure when youYou experience this pressure when you dive to the bottom of a pool, drive up adive to the bottom of a pool, drive up a mountain, or fly in a plane.mountain, or fly in a plane.
- 19. PressurePressure PressurePressure is the magnitude of the force on ais the magnitude of the force on a surface per unit area.surface per unit area. PascalPascal’’s principle states that pressure applied tos principle states that pressure applied to a fluid in a closed container is transmitteda fluid in a closed container is transmitted equally to every point of the fluid and to theequally to every point of the fluid and to the walls of the container.walls of the container. P = F A pressure = force area
- 20. PressurePressure The 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 x 101055 Pa.Pa. This gives us another unit for pressure, theThis gives us another unit for pressure, the atmosphere, where 1atmosphere, where 1 atmatm = 1.01 x 10= 1.01 x 1055 PaPa
- 21. PascalPascal’’s Principles Principle When you pump a bike tire, you applyWhen you pump a bike tire, you apply force on the pump that in turn exerts aforce on the pump that in turn exerts a force 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 on the pump but also against the walls of thethe pump but also against the walls of the tire.tire. As a result, the pressure increases by anAs a result, the pressure increases by an equal amount throughout the tire.equal amount throughout the tire.
- 22. PascalPascal’’s Principles Principle A hydraulic lift usesA hydraulic lift uses Pascal's principle.Pascal's principle. A small force is appliedA small force is applied (F(F11) to a small piston of) to a small piston of area (Aarea (A11) and cause a) and cause a pressure increase on thepressure increase on the fluid.fluid. This increase in pressureThis increase in pressure ((PPincinc) is transmitted to the) is transmitted to the larger piston of area (Alarger piston of area (A22)) and the fluid exerts aand the fluid exerts a force (Fforce (F22) on this piston.) on this piston. F1 F2 A1 A2 2 2 1 1 A F A F Pinc == 1 2 12 A A FF =
- 23. ExampleExample The small piston of a hydraulic lift has anThe small piston of a hydraulic lift has an area of 0.20 marea of 0.20 m22 . A car weighing 1.20 x 10. A car weighing 1.20 x 1044 N sits on a rack mounted on the largeN sits on a rack mounted on the large piston. The large piston has an area ofpiston. The large piston has an area of 0.90 m0.90 m22 . How much force must be applied. How much force must be applied to the small piston to support the car?to the small piston to support the car?
- 24. SolutionSolution Plug and Chug:Plug and Chug: FF11 = (1.20 x 10= (1.20 x 1044 N) (0.20 mN) (0.20 m22 / 0.90 m/ 0.90 m22 )) FF11 = 2.7 x 10= 2.7 x 1033 NN 2 2 1 1 A F A F = 2 1 21 A A FF =
- 25. Your Turn IIYour Turn II In a car lift, compressed air exerts a force on aIn a car lift, compressed air exerts a force on a piston with a radius of 5.00 cm. This pressure ispiston with a radius of 5.00 cm. This pressure is transmitted to a second piston with a radius oftransmitted to a second piston with a radius of 15.0 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 x 101044 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 the personperson’’s ears fail tos ears fail to ““poppop””. The radius of each. The radius of each ear drum is 0.40 cm. The pressure of theear drum is 0.40 cm. The pressure of the atmosphere drops from 10.10 x 10atmosphere drops from 10.10 x 1055 Pa at thePa at the bottom 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 and outer 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 each eardrum?eardrum?
- 26. PressurePressure Pressure 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 with depth.depth. ( ) ρ= + × × 0 absolute pressure = atmospheric pressure + density free-fall acceleration depth P P gh
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- 28. Fluids in MotionFluids in Motion Section 3Section 3
- 29. Fluid FlowFluid Flow Moving fluids can exhibitMoving fluids can exhibit laminarlaminar (smooth)(smooth) flow orflow or turbulentturbulent (irregular) flow.(irregular) flow. Laminar Flow Turbulent Flow
- 30. Fluid FlowFluid Flow AnAn ideal fluidideal fluid is a fluid that has no internalis a fluid that has no internal friction or viscosity and is incompressible.friction or viscosity and is incompressible. The ideal fluid model simplifies fluidThe ideal fluid model simplifies fluid--flowflow analysisanalysis
- 31. Fluid FlowFluid Flow No real fluid has all the properties of anNo real fluid has all the properties of an ideal fluid, it helps to explain the propertiesideal fluid, it helps to explain the properties of real fluids.of real fluids. Viscosity refers to the amount of internalViscosity refers to the amount of internal friction within a fluid. High viscosity equalsfriction within a fluid. High viscosity equals a 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 the fluid are constant.fluid are constant.
- 32. Principles of Fluid FlowPrinciples of Fluid Flow The continuity equation results fromThe continuity equation results from conservation of mass.conservation of mass. Continuity equation:Continuity equation: AA11vv11 == AA22vv22 AreaArea ×× speed in region 1 = areaspeed in region 1 = area ×× speed in region 2speed in region 2
- 33. Principles of Fluid FlowPrinciples of Fluid Flow The speed of fluid flowThe speed of fluid flow depends on crossdepends on cross-- sectional area.sectional area. BernoulliBernoulli’’s principles principle states that the pressurestates that the pressure in a fluid decreases asin a fluid decreases as the fluidthe fluid’’s velocitys velocity increases.increases.
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