ch 14. fluid mechanicsliu.physics.ucdavis.edu/phy9b/fluid.pdf · ch 14. fluid mechanics. liu ucd...
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Liu UCD Phy9B 07 1
Ch 14. Fluid Mechanics
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14-1. DensityDensity ρ=m/V - kg/m3
1g/cm3=1000 kg/m3
Intrinsic to a material, independent of size & shape
Specific gravity ρ/ ρwater
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14-2. Pressure in a FluidPressure in a fluid of uniform density (Static Case)
p2 - p1=-ρg(y2-y1)p=po+ ρgh
Pressure is the same for any 2 points at the same level in the fluid.
Gauge pressure:Excess pressure above atmospheric pressure
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Pascal’s LawPressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the container.
2
2
1
1
AF
AFp ==
11
22 F
AAF =
Application in hydraulic lift
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14-3. Buoyancy
Archimedes’ Principle:When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.
B=ρfluid gVdisplaced fluid
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Surface Tension
Liquid alonetends to minimize its surface area
Liquid in contact with solid
Wetting Non-wetting
Capillarity
Wetting Non-wetting
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14-4. Fluid Flow
Laminar flow: adjacent layers of fluid slide smoothly & flow steadily
Turbulent flow:irregular & chaotic flowno steady-state pattern
Continuity Equation
Incompressible fluid:dm1=dm2 (ρA1v1dt= ρA2v2dt)A1v1= A2v2
Volume flow rate: dV/dt=Av
Ideal fluid: incompressible (ρ const.) & no internal friction (viscosity)
Denser streamlines, higher speed
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14-5. Bernoulli’s EquationFor incompressible, steady flow of a fluid with no viscosity
2222
2111 2
121 vgypvgyp ρρρρ ++=++
Links pressure p, height y, flow speed v
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Special Cases of Bernoulli’s Equation
Special case #1:
p1=p2
22
11 21 gyvgy ρρρ =+
)(2 121 yygv −=Torricelli’s theorem:
Special case #2:Same height:
222
211 2
121 vpvp ρρ +=+
Where the speed is high, the pressure is low.
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Applications of Bernoulli’s Principle
Dec. 17, 1903: First flights by Wright brothers.