Bernoulli equation with the appropriate adjustments
Posted: Tue Jun 12, 2007 12:21 am
Hi guys!
i read the thread about fluid motion inside a watergun, and how it 'forces' the weapon back when the trigger is pulled..
without getting much into big mechanical details (otherwise this would be a neverending post..) the first thing you should know about is the Reynolds adimensional number.
this number, Re, is a ratio between the physical effect of fluid inercia vs. viscosity.
Re=(fluid density*fluid average speed*vessel diameter)/fluid viscosity
(fluid moves in a very complicated way, if you imagine a vessel, the fluid adjacent to the vessel has zero velocity, and the maximum velocity is in the axis of the tube. kind of a parabolic cone. that's why i said fluid average speed.)
this Reynolds number indicates whether your fluid motion is laminar or turbulent.
for Re<2000 (approximately) fluid motion is laminar. Above 4000 is turbulent.
why is Re important? because it is the simplest way to know if you are minimizing turbulence, which gives you more momentum at the nozzle exit
another important aspect:
the Bernoulli equation --> Bernoulli was a guy with a lot of time in his hands who came up with the theory that in ideal conditions, a stream of fluid maintains its mechanical energy from point A to B:
Pressure Energy Contribution + Dynamic Pressure Energy Contribution (fluid inercia,.. kind of.) + Gravity Energy Contribution = constant
in each point of fluid each one of the contribution type may vary, but its sum is a constant.
SuperSoakers ARE NOT built with ideal vessels you all know that
From point A to B:
tubes have rough surface that create turbulence hence dissipating some of the momentum mostly into heat. some of the turbulence creates localized back flow areas that reduce overall power in the fluid streamline;
intersections, nozzles entrances, etc.. all vessel junctions with a significant diameter ratio (D/d > 1.2 +\-) will create a special turbulence called 'vena contracta' effect. specially at the nozzle exit where you can find a lot of 'walls'. this is responsible for a water stream that easily loose its cylindrical shape.
while a localized turbulence with a 'vena contracta' effect has a contribution of K=0.5 to 3 or 5 to the overall power loss, a complicated valve can have a K value of 150 to 210. (don't ask me what is K, i mentioned it just as a way to compare, its way too complicated to write it all here )
the thing is, these turbulence effects are greatly amplified by a big Re value.
phew.. that's a lot of stuff here
oh and by the way, Navier-Stokes equations are best used in low Re values , or in typical fluid motion such as laminar rotation or others.
i hope this is of some use here !
c-ya
i read the thread about fluid motion inside a watergun, and how it 'forces' the weapon back when the trigger is pulled..
without getting much into big mechanical details (otherwise this would be a neverending post..) the first thing you should know about is the Reynolds adimensional number.
this number, Re, is a ratio between the physical effect of fluid inercia vs. viscosity.
Re=(fluid density*fluid average speed*vessel diameter)/fluid viscosity
(fluid moves in a very complicated way, if you imagine a vessel, the fluid adjacent to the vessel has zero velocity, and the maximum velocity is in the axis of the tube. kind of a parabolic cone. that's why i said fluid average speed.)
this Reynolds number indicates whether your fluid motion is laminar or turbulent.
for Re<2000 (approximately) fluid motion is laminar. Above 4000 is turbulent.
why is Re important? because it is the simplest way to know if you are minimizing turbulence, which gives you more momentum at the nozzle exit
another important aspect:
the Bernoulli equation --> Bernoulli was a guy with a lot of time in his hands who came up with the theory that in ideal conditions, a stream of fluid maintains its mechanical energy from point A to B:
Pressure Energy Contribution + Dynamic Pressure Energy Contribution (fluid inercia,.. kind of.) + Gravity Energy Contribution = constant
in each point of fluid each one of the contribution type may vary, but its sum is a constant.
SuperSoakers ARE NOT built with ideal vessels you all know that
From point A to B:
tubes have rough surface that create turbulence hence dissipating some of the momentum mostly into heat. some of the turbulence creates localized back flow areas that reduce overall power in the fluid streamline;
intersections, nozzles entrances, etc.. all vessel junctions with a significant diameter ratio (D/d > 1.2 +\-) will create a special turbulence called 'vena contracta' effect. specially at the nozzle exit where you can find a lot of 'walls'. this is responsible for a water stream that easily loose its cylindrical shape.
while a localized turbulence with a 'vena contracta' effect has a contribution of K=0.5 to 3 or 5 to the overall power loss, a complicated valve can have a K value of 150 to 210. (don't ask me what is K, i mentioned it just as a way to compare, its way too complicated to write it all here )
the thing is, these turbulence effects are greatly amplified by a big Re value.
phew.. that's a lot of stuff here
oh and by the way, Navier-Stokes equations are best used in low Re values , or in typical fluid motion such as laminar rotation or others.
i hope this is of some use here !
c-ya