Bernoulli's
Principle, part of Hydrodynamica, is based on the principle of
conservation of energy and say that, if velocity/speed of a fluid
gets increased, the pressure decreases. So if a fluid gets to a
bottleneck it has to speed up to bring up the same
amount of flow. Now by speeding up, there is a higher energy used for
velocity, so there is less energy left for pressure(->
conservation of energy). Therefore the pressure drops. When the fluid
comes to a big area, the fluid has to slow down, to bring up the same
amount of flow. Because of slowing down, there is less energy used
for velocity. The spare energy goes into pressure, so the pressure
increases.
His Formula is:
“v”
is
the speed; “g” is the acceleration due to gravity; “z” is the
elevation; “p” is the pressure and “ρ”
is the density.
But
Bernoulli did his experiments with liquids that are not compressible.
Now there is the question if his principle also works for
compressible fluids like air, or if then happens something that
changes the outcome. Up to speeds of 300 kph compressible and
incompressible fluids react nearly same, but from this point on a
relevant amount of energy is used to compress the fluid or gets
released by decompressing the fluid, instead of using or releasing
all the energy for/from increasing/decreasing the pressure. So now a
new formula is needed. This formula is based on the first formula
from Bernoulli and Newton's laws of motion. It is:
“p”
is the pressure
“ρ”
is the density
“v”
is the flow speed
“Ψ” is the potential associated with the conservative force field, often the gravitational potential
“Ψ” is the potential associated with the conservative force field, often the gravitational potential
