>
>
> From: "Stefan Trethan" <stefan_trethan@...>
>Subject: Re: Sprayer pressure
>
>ok, time for maths.
>
>according to a formula i found on the web a 50mm dia tube spinning at
>1000rpm experiences 274m/s2 or 28g on the inside edge.
>so if there is, say 1cm high water over 1cm2 that weighs 1g it should
>produce about 28g of pressure on the wall.
>1 bar is 1kg per square cm, so the pressure created by the spinning tube
>is .... nothing?
>
>
Stephan
Just as a quick estimate, your not producing NO pressure, just .28
bar. :^)
You need to generate at least (1000/2.5) = 400 Gs to make 2.5 cm fluid
height give you one bar.
This is giving you credit for a constant G with depth (which you don't
get, you either get linear increase with r or even r^2).
If it is linear, you need 2kG at the rim to get 1 bar.
American ignorance - Is bar an atmosphere, or does it just work out close?
Stupid Richard - it just works out close - 10 meters is ~32.8 ft H2O, 1
atm is ~ 35 ft H2O
- REMEMBER - the following is all first order approximation, so my
numbers are only order of magnitude! (at best)
1000 RPM is only 16&2/3 per second
A 0.05 meter diameter circle only has a 0.157 meter circumference.
16.67∗0.157 is only 2.62 mps velocity at the inside rim.
Rotating around the Z axis, a point on the rim gets accelerated (in the
X axis) from V=0 to V=2.62 to V=0 to V=-2.62 to V=0 in 1 revolution.
This means as a lower bound, (I'm only dealing in one axis, not two, as
I should be) the point gets accelerated from 0 to 2.62mps 4 times per
revolution. so, 2.62 mps ∗ 16.67 rps ∗ 4 per revolution = 174.5 mps^2
divide by 9.8 mps^2 = 17.8 G.
This tells me the 28G you calculated is the right order of magnitude.
I guess if I were better at the Calculus, I'd have whipped out the right
answer.
Maybe the outflow of the fluid is the result of it moving tangentially
at 2.6 mps, not because it's squirting out under pressure.
It kind of makes sense if you look at the numbers.
I wish I remembered half of what I've forgotten in fluid mechanics, I
could understand it better and give a better explanation.
As far a nozzles go, in the US, Home Despot has started carrying 1/2 and
1/4 inch irrigation equipment, mass produced plastic (not sure what
kind), with all sorts of nozzles - mist, 45, 90 180 and 360 sprayers,
all for 5 for two dollars kind of prices. They screw right into 1/4
inch tubing, and are made to screw into the side of 1/2 inch tube. If
you are interested, and can't get it over there (I hope the EU is not as
obsessive about their lawns as we are), I'd be willing to mail you an
assortment. I think that USPS has an international 3 day for less than
$20, and these things don't weigh much.
LMK
Thanks
Richard.
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