daniel bernoulli david applegate cassandra diamond erin ryan tiffany liang
TRANSCRIPT
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Daniel Bernoulli
David ApplegateCassandra Diamond
Erin RyanTiffany Liang
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Background• Born on February 8th,
1700o Groningen, Netherlands
• Swiss mathematician and physicist
• Leonhard Euler• Received Bachelor’s
degree at 15 and Master’s degree at 16
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Background• Bernoulli Family
o 8 family members were mathematicians
• University of Baselo Medicine, metaphysics, and natural philosophy
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Studies• Bernoulli’s Equation• Bernoulli’s Principle• Kinetic Theory of Gases
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Bernoulli’s Equation
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Bernoulli’s Equation• Mathematical model of fluid flow through a
conduit• Based on the conservation of energy law applied
to the fluid• This equation can be applied to incompressible
fluids as well as compressible gases or fluids moving at low Mach Numbers
• Bernoulli first published this equation in Hydrodynamica (1783).
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Energy Applied to the Fluid
Energy Type Formula
o Enthalpic
o Gravitational
o Kinetic
o Friction Loss
o Work
The Bernoulli equation concerns itself with incompressible (constant density) and adiabatic (no heat applied/removed) fluid flow.
Combining Terms results in the Bernoulli Equation
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Derivation of Bernoulli’s Equation
• Differential energy balance:
• Plugging in equations for entropy and enthalpy:
• Gives:
• Integrate:
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The Incompressible Fluid Bernoulli Balance
Note: P2, P1, V2,V1 terms are initial (1) and final (2) states.
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Bernoulli’s Principle
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What is Inviscid Flow?
-Idealized form of fluid-Supposes that fluid has a viscosity of 0-Looks like laminar, but drag has no effect
Standard Laminar Inviscid Flow
Images courtesy of me spending way too long in MS Paint
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Inviscid Flow Around Objects
Around a sphere Around a wing
Images courtesy of http://www.allstar.fiu.edu
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So are you going to talk about Bernoulli?
Bernoulli's Principle
-For inviscid flows, kinetic and potential energy are exchangeable
-That means as pressure changes, velocity changes to compensate (and vice versa)
-Forms the backbone of the Bernoulli Equation
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Bernoulli’s Kinetic Theory
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KINETIC THEORY
• In his most famous work,
Hydrodynamica , Bernoulli was
the first to postulate on the
kinetic theory of gases.
• This included • the idea that pressure is a result
of the collisions between gas molecules and the walls of a container
• the theorem that temperature is related to the velocity, or the kinetic energy of the molecules in a substance.
P1 = atmospheric pressure
PS = pressure when piston at height s
𝑃𝑆𝑃1
=𝑉 2
𝑠
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There was not enough experimental evidence at the time to quantify a relationship between temperature and average molecular velocity, but an equation would eventually be developed. This idea is also the basis of the identification of an absolute temperature scale.
Maxwell and Boltzmann later expanded on Bernoulli’s theory and used statistical methods to determine a more qualitative relationship between temperature and average translational kinetic energy of molecules.
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Aerodynamics Application
• An airfoil on the wing of an airplane forces the air along the upper surface to travel a longer distance, increasing its velocity.
• According to Bernoulli’s principle, this increase in velocity causes a decrease in pressure and creates lift.
• The flaps on the wings of planes perform a similar function.
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Source Citation• Levermore, Dave. (2001):
<http://www2.math.umd.edu/~lvrmr/History/EarlyTheories.html>.
• Whitaker, Robert D. "University of South Florida." University of South Florida. 56. (1979): 315-318. <http://pubs.acs.org/doi/pdfplus/10.1021/ed056p315>.
• Friedman, Erich. (2005): <http://www2.stetson.edu/~efriedma/periodictable/html/B.html>.