Lecture 10-11: Bernoulli Flashcards
What is the universal rule (conservation and continuity laws)?
in a closed system, mass, momentum (mass x velocity), and energy must be the same over time (conserved)
What is a closed system?
physical space that does not allow for the transfer of mass or energy into or out of the system
When is potential energy greatest?
at greatest height
When is kinetic energy greatest?
at greatest velocity
What happens to energy in a pendulum?
energy is conserved
potential energy is converted to kinetic energy, and vice versa
What energy is in a fluid? (3)
- potential energy density (⍴gh)
- kinetic energy density (½⍴v^2) – dynamic pressure
- pressure energy density (P) – static pressure
Compare energy in a solid vs. fluid.
potential energy (mgh) – uses mass
potential energy density (⍴gh) – uses density
etc.
- mass is a good way to deal with solid objects (ie. easy to define the mass of an organism), BUT it is not easy to apply the idea of a discrete mass to unbounded fluid flows (ie. what mass of water is interacting with the organism)
- when describing the energy present in a fluid, density (mass/volume) of the fluid is used
What is Bernoulli’s theorem?
describes how the total energy of a moving fluid is equal to the sum of the pressure, potential energy, and kinetic energy
total fluid energy = P + ⍴gh + ½⍴v2
What can Bernoulli’s theorem be used for? What assumptions must be made?
possible to use theorem to determine how these different components of a fluid’s energy must change to satisfy the law of conservation of energy in a moving fluid
for this to work, it requires some simplifying assumptions to be made about the fluid:
- flow is inviscid (ie. moves without drag/friction)
- flow is incompressible (low velocity)
- flow is constant (volume/time)
- flow is laminar (no turbulence)
What is static pressure (P)?
pressure at some point in a fluid
- pressure is exerted equally in all directions within the fluid (scalar force)
Why is it called static pressure, not just pressure?
to distinguish it from dynamic pressure
In what direction does static pressure (P) act?
acts perpendicular (normal) to the surface of any object in the fluid
What is kinetic (dynamic) energy?
energy possessed by a fluid in motion
equivalent to the amount of pressure that would be exerted by the moving fluid if it collided with an object and stopped
What is potential pressure energy?
energy due to the fluid’s location above some (arbitrary) ground level
When is total energy (sum of static pressure, kinetic dynamic energy, and potential energy) always constant?
in a system where fluid flow is inviscid, incompressible, constant, and laminar
