David Applegate Cassandra Diamond Erin Ryan Tiffany Liang Background Born on February 8 th 1700 Groningen Netherlands Swiss mathematician and physicist Leonhard Euler Received Bachelors degree at 15 and Masters degree at 16 ID: 322416
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Slide1
Daniel Bernoulli
David Applegate
Cassandra Diamond
Erin Ryan
Tiffany LiangSlide2
Background
Born on February 8
th
, 1700Groningen, NetherlandsSwiss mathematician and physicistLeonhard EulerReceived Bachelor’s degree at 15 and Master’s degree at 16Slide3
Background
Bernoulli Family
8 family members were mathematicians
University of BaselMedicine, metaphysics, and natural philosophy Slide4
Studies
Bernoulli’s Equation
Bernoulli’s
PrincipleKinetic Theory of Gases Slide5
Bernoulli’s EquationSlide6
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 NumbersBernoulli first published this equation in Hydrodynamica (1783).Slide7
Energy Applied to the Fluid
Energy Type
FormulaEnthalpicGravitational
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 EquationSlide8
Derivation of Bernoulli’s Equation
Differential energy balance:
Plugging in equations for entropy
and enthalpy
:
Gives:
Integrate:
Slide9
The Incompressible Fluid
Bernoulli Balance
Note: P2, P1, V2,V1 terms are initial (1) and final (2) states. Slide10
Bernoulli’s PrincipleSlide11
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 PaintSlide12
Inviscid Flow Around Objects
Slide13
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 EquationSlide14
Bernoulli’s Kinetic
TheorySlide15
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
Slide16
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.Slide17
Aerodynamics Application
An airfoil on the wing of an airplane forces the air along th
e 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.Slide18
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>.