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Daniel Bernoulli

Daniel Bernoulli. David Applegate Cassandra Diamond Erin Ryan Tiffany Liang. Background. Born on February 8 th , 1700 Groningen, Netherlands Swiss mathematician and physicist Leonhard Euler Received Bachelor’s degree at 15 and Master’s degree at 16. Background. Bernoulli Family

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Daniel Bernoulli

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  1. Daniel Bernoulli David Applegate Cassandra Diamond Erin Ryan Tiffany Liang

  2. Background • Born on February 8th, 1700 • Groningen, Netherlands • Swiss mathematician and physicist • Leonhard Euler • Received Bachelor’s degree at 15 and Master’s degree at 16

  3. Background • Bernoulli Family • 8 family members were mathematicians • University of Basel • Medicine, metaphysics, and natural philosophy

  4. Studies • Bernoulli’s Equation • Bernoulli’s Principle • Kinetic Theory of Gases

  5. Bernoulli’s Equation

  6. 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).

  7. Energy Applied to the Fluid Energy TypeFormula • Enthalpic • Gravitational • Kinetic • Friction Loss • 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

  8. Derivation of Bernoulli’s Equation • Differential energy balance: • Plugging in equations for entropy and enthalpy: • Gives: • Integrate:

  9. The Incompressible Fluid Bernoulli Balance Note: P2, P1, V2,V1 terms are initial (1) and final (2) states.

  10. Bernoulli’s Principle

  11. 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

  12. Inviscid Flow Around Objects Around a sphere Around a wing Images courtesy of http://www.allstar.fiu.edu

  13. 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

  14. Bernoulli’s Kinetic Theory

  15. KINETICTHEORY 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

  16. 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.

  17. 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.

  18. 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>.

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