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FLUID PROPERTIESFLUID PROPERTIESChapter 2

CE319F: Elementary Mechanics of Fluids

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Elasticity (Compressibility)

VdpdV VdpE

dVv

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• If pressure acting on mass of fluid increases: fluid contracts

• If pressure acting on mass of fluid decreases: fluid expands

• Elasticity relates to amount of deformation for a given change in pressure

Ev = bulk modulus of elasticity

Small dV/V = large modulus of elasticity

ddp

VdVdp

Ev How does second part of equation come about?

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ExampleBased on the definition of Ev and the equation of state, derive an equation for the modulus of elasticity of an ideal gas.

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Vapor Pressure (Pvp)• Vapor pressure of a pure liquid = equilibrium partial pressure of the

gas molecules of that species above a flat surface of the pure liquid– Concept on board– Very strong function of temperature (Pvp up as T up)– Very important property of liquids– When Pvp exceeds total air pressure applied at surface, liquid will boil.

• Pressure at which a liquid will boil for a given temperature– At 10 oC, vapor pressure of water = 0.012 atm = 1200 Pa– If reduce pressure to this value - get boiling of water – Formation of cavitation bubbles – Harm to pipes, pumps, turbines, propellers

• If Pvp > 1 atm compound = gas

• If Pvp < 1 atm compound = liquid or solid

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Vapor Pressure (Pvp)Vapor Press. vs. Temp.

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100

Temperature (oC)

Vap

ro P

ress

ure

(kP

a)

Vapor pressure of water (and other liquids) is a strong function of temperature.

Water

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Vapor Pressure (Pvp) - continued

OHvp

OH

P

PxRH

2

2

,

%100

Pvp,H2O = Pexp(13.3185a – 1.9760a2 – 0.6445a3 – 0.1299a4)

P = 101,325 Pa a = 1 – (373.15/T) T = oK

valid to +/- 0.1% accuracy for T in range of -50 to 140 oC

Equation for relative humidity of air = percentage to which air is “saturated” with water vapor.

How does RH affect drying of building materials, and why? Implications?

How does RH affect dust mites? Implications?

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300 m

Dust Mites

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9

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Example (HW!): Relative HumidityThe relative humidity of air in a room is 80% at 25 oC.

(a) What is the concentration of water vapor in air on a volume % basis?

(b) If the air contacts a cold surface, water may condense (see effects on next slide). What temperature is required to cause water condensation?

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Example: Relative HumidityContinuedContinued

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 5 10 15 20 25 30 35

degrees C

Pvp

(P

a)