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Lecture 05_Phys122

# Lecture 05_Phys122 - Topic#1 Fluid sciences Bertrand...

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Bertrand Dano Topic#1: Fluid sciences

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Bertrand Dano The Bernoulli equation P + ½ ρ U2 + ρ gh = cte P 1 + ½ ρ 1 U 1 2 + ρ 1 gh 1 = P 2 + ½ ρ 2 U 2 2 + ρ 2 gh 2 The Bernoulli Equation is Listed in Michael Guillen's book "Five Equations that Changed the World: The Power and Poetry of Mathematics" Daniel Bernoulli (1700-1782) •Newton’s Second Law is the Governing Equation •Applied to an Idealized Flow and Assumes Inviscid Flow •There are numerous assumptions •“Most Used and Abused Equation”
Bertrand Dano Application of Bernoulli’s equation The Pitot tube Pitot tube Boeing 747 Pitot tube Cessna 152 Pitot tube P atm P atm U U Measure the total pressure Measure the static pressure

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Bertrand Dano P 1 + ½ ρ U 1 2 = P 2 + ½ ρ U 2 2 Application of Bernoulli’s equation The Pitot tube Pitot tube P atm P atm U U P 1 + ½ ρ U 1 2 + ρ 1 gh 1 = P 2 + ½ ρ U 2 2 + ρ 2 gh 2 1 2 ρ ) ( 2 1 2 1 P P U - = Velocity can be obtained by measuring the difference between the total and static pressure Measure the total pressure Measure the static pressure
Bertrand Dano Application of Bernoulli’s equation P 1 + ½ ρ U 1 2 + ρ 1 gh 1 = P 2 + ½ ρ U 2 2 + ρ 2 gh 2 2 1 P atm P atm U 2 H P + ½ ρ U2 + ρ gh = cte ρ g(h 2 -h 1 ) = ½ ρ U 2 gH = ½ U 2 2gH U = U 1 very small Physical Interpretation: All the particles potential energy is converted to kinetic energy assuming no viscous dissipation.

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Bertrand Dano Pressure driven jet Laminar jet Instabilities
Bertrand Dano Pressure driven jet Laminar jet Surface tension Turbulent jet

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Bertrand Dano Pressure driven jet As H decreases, U decreases too 2gH U =
Bertrand Dano Fluid properties: surface tension & viscosity

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Bertrand Dano LIQUID Vapor Attractive force between molecules At the interface between a liquid and a gas or two immiscible liquids, forces develop forming an analogous “skin” or “membrane” stretched over the fluid mass which can support weight.
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Lecture 05_Phys122 - Topic#1 Fluid sciences Bertrand...

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