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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.