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Re: Spraybars

The answer to your question is quite a complex one. I will attempt to
contribute what I can.
In reply to your parallel with the pipeline water distribution example,
the realistic part is in fact that, the secondary lines do not in fact
get equal flow. This is where secondary pumping stations come in and
regular testing is needed. Engineers and water companies perform
pressure testing at certain places in the lines at relatively (or in
some cases, not regularly enough) intervals in order to assertain
whether modifications to the pipelines and implementation of booster
stations will be needed. Also not *all* houses are using water at the
same time, so what is quite often done is a rough 'average' of the usage
through the area at any one point in time. All the water company does is
try to supply that usage (plus some safety factor) to the major
junctions of that region and hope that it suffices for the people in
that region 99.99% of the time. Not all houses receive equal pressure
exactly - this is why in poorly serviced regions there can be
fluctuations (very annoying when you need are looking forward to that
morning shower to wake you up!).
For your spray bar itself, the fluid dynamics surrounding this is more
complex than a simple formula. For starters, depending on your pipe, and
manufacturer, the internal pipe relative roughness will vary. The
diameter and relative roughness of the pipe will affect the Reynolds
number - and therefore will be a transition between complete laminar
flow through the pipe to a proportion of laminar and turbulent flow
(also adding difficulty in calculations). The differences in laminar and
turbulent boundary layers (and relative equations needed for each one)
will create complications. I don't know whether your system is a large
system operating at cubic metres per hour, or a small system consisting
of just a canister filter, but the equations actually become more
complex the smaller the system is. Also you have to consider
interactions between the holes themselves and the fluid. There will be a
vena contractor at each hole, varying in size depending on hole size,
causing eddys and swirling. Therefore the diameter of the outlets will
also cause complications. I could go on but the specifics are probably
not of much use. Don't get me wrong, it would be possible to do all the
necessary theoretical calculations - but it would be as impractical as
attempting to calculate theoretically the drag coefficient of a car. It
could be done, but why bother? Make a model, or prototypes and test them
in similitude. Much quicker.
What I highly recommend is to not worry about calculations as such, but
just make a variety of them out of the pipe that you are going to use,
until you get it right. The dynamics surrounding the problem are too
complex. I believe that getting the 'perfect' spray bar is almost
impossible anyway depends on too many parameters that are not
necessarily controllable. You may have to be content to just have some
holes a bit more pressurised than others :)
Hope this helps!
Adam Shaw

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