Biopowered - vegetable oil and biodiesel forum
General => Wiki and forum discussion => Topic started by: therecklessengineer on August 11, 2012, 01:50:52 PM
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Could I make the suggestion that the venturi formula be simplified a bit?
Given that the whole thing is an approximation anyway, and you further that approximation by taking pi = 3, then the whole thing cancels to simply sqroot(flowrate).
Even if you don't take pi = 3, then there is simplification to be had.
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Makes sense. I guess the original formula was derived based on flow through a cross sectional area, which this is the inverse of. I wonder how precise it really is - I guess only Jim could call that one.
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Good to have someone a bit brainy looking through the wiki!
Jim's pretty good at sums, I'm surprised he didn't simplify things.
Me, I'm not good at sums but I've worked a couple of examples and the throat diameter comes out to within one or two points of a millimetre.
Unless you are drilling the throat, I don't think mere mortals could make a venturi to that degree of accuracy anyway!
Why don't we put both formulas up?
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I did some research a while back and went quite in depth.
My conclusion was that there is no analytical solution for maximising the vacuum produced by a venturi. By analytical, I mean working it out on a bit of paper using algebra only. There are quite simply too many variables.
Fluid dynamics is a horrifically complex subject with what I'd describe as 'improper' maths. As an engineer I like pure maths - situations you can analyse and describe in precise mathematical terms. Fluid dynamics has very little of this - it's all manipulation of experimental data.
So, by doing multiple experiments it might be possible to deduce a relationship between throat diameter and flow rate - that appears to be what Jim has done, although when I asked him for his data on which he based his formula I got a very short response.
You could potentially have a numerical solution - which rely on number crunching (i.e. computers) to produce an answer. This might produce a solution to a particular problem (combination of pipework, pump curve, venturi dimensions, discharge pipework, fluids used etc etc) but not a general one.
Anyhow, however Jim has ended up with the 'formula' it has been proved time and time again to produce venturi dimensions that work. How optimal they are is difficult to show without making several and testing them. I'd suggest that they are certainly in the right ballpark.
In any case, due to the approximate nature of the whole thing, I'd feel entirely justified in reducing the whole thing to sqrt(flow rate). The differences in dimensions will have negligible effect.
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With your mathematical expertise, would you mind taking a look at this page ... http://www.biopowered.co.uk/wiki/Cone_bottoms_for_tanks
I started the page and Jim altered some of the formula at the top of the page, but I think what he did would only suit a 45° cone. He then said there was an easer way without a formula and asked that I produce the third graphic, I think I can see where he was going but the page has died a death since then.
I know JTF have a calculator, but we all feel the wiki should be original work. If you could come up with a formula that would be fantastic. I'll happily alter the graphics to suit and I'm sure Tony would put together our own calculator which we could link to the page.
I'm away for the next week, but I'll alter the venturi page when I get back.
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Only a week :'(,the courts are getting too lenient!
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No, no they are PAYING me to go!
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No problem - but I'll need to find some quiet time when I can sit and work it out.
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I've updated the wiki to mention the simplified formula, and also how to use it (was lacking in units somewhat!). Julian please could you update the formula graphic?
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I had a look at general solutions for cones last night. None of what's quoted here is my final answer - I need to go over them again to prove they're correct.
Using dimension labels from the wiki page. Finding L given D is fairly simple for any given angle a: L=D/(2cos(a)). Or if you want the diameter of your starting sheet: L_2=D/cos(a) The hole in the middle follows the same formula. A general solution for angle b is getting a bit harder b=(2pi(1-cos(a))) - answer in radians. The version in degrees starts to look nasty.
And I tried to find the chord length of the section we need to remove. I figured this is probably a good measurement to use as we can measure it easily. Measuring around the circumference of a circle is more difficult! Anyhow, I got: z=D/(4picos(a)(1-cos(a))). This is getting quite technical, and I need to look at this further because I'm sure there's a trigonometric identity that I've forgotten along the way that'd help here.
Given that this is getting all a bit technical, how about adding a 'cone calculator' to the wiki? Can we insert JS or PHP? I have little experience with either - but I might be able to code something. Or we could fall back on an excel spreadsheet...
P.S. Just remembered an identity that might help (and feel a little foolish that I missed it) - I'll look again later.
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If you have a peer at the Tools menu above, you'll see the calculators there are just javascript on a static page (with some template wrappers for forum integration). So we definitely can make a calculator.
If you finalise the formula I can certainly put something together.
Unfortunately the wiki doesn't allow forumulaes on pages directly as it's a massive security risk, but no problem with static, templatised pages served as part of the forum.
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I never noticed those calculators there! Very useful.
These are my final answers. I've verified them for a single case, but it'd be useful if someone else could as well just in case I've copied them down wrong or something equally idiotic.
The chord z is as simple as I can make it - but I'm afraid it still looks pretty horrendous.
I also looked at the required surface area to manufacture each cone dependent on angle. A sketch of how the area required (including the section we chop out) varies with cone angle is shown in the graph. I was expecting a minimum at zero and infinite at 90 degrees, but I was surprised by how steep the cone can be without really affecting the area much. Essentially you aren't going to use much more material for a 45 degree cone than a 30 degree. It will start getting much bigger as you approach 60 degrees though. Units are arbitrary, so no relationship to anything except each other.
And finally, Jim's venturi formula simplifies exactly to: Throat size = 2*sqrt((5*Fr)/(6*pi)). Which I think is nicer (although not quite as nice as sqrt(Fr) ;) )
[attachment deleted by admin]
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Thanks James. I hope to have a look at those in a bit more detail later today.
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Ok, venturi formula's done.
I also changed the old formula, the idiot who did it originally had a coloured outline round the pi symbol.
Do we need alternative graphics for the cone page?
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Any further progress with the cone formulae?
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Forgot all about it. I'll start a page now - may need a funky diagram from Julian.
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Your wish is my diagram ... provided you don't want it quickly.
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I want it on my desk by yesterday!
Seriously, it'll take a while to sort the page anyway, and we need to work out what to label it with so no rush :)
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Step one complete - template and start of functionality added
http://www.biopowered.co.uk/forum/tools/cone.php
The rest tomorrow hopefully :)
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As an input, besides the drum dia surely you only need either the cone height or the angle, or are you giving people the option of either?
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Maybe not clear on the page but drum dia and angle are inputs, height is derived from this (just so happens that 60 degrees gives same dia and height).
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I'd recommend against making a cone as steep as 60 degrees for material cost reasons. You'll need a huge sheet of metal!
30 and 45 degrees aren't huge amounts, but over 50 and you're looking at an exponential increase in size.
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Good to have some defaults :) Any ideas on what is the most common drum diameter?
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Now then...for the laymen among us who are not mathmatically adept could someone please explain the two venturi formulas.
I have always made venturi's to the throat size's that Jim gave me ie 40/60 =8mm, 80=9.2 mm, 120= 10.8mm
I don't pretend to understand the formula's listed in the wiki but would appreciate being shown, with examples, what everything means and how it's calculated.
Thanks
Nige
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Now then...for the laymen among us who are not mathmatically adept could someone please explain the two venturi formulas.
I have always made venturi's to the throat size's that Jim gave me ie 40/60 =8mm, 80=9.2 mm, 120= 10.8mm
I don't pretend to understand the formula's listed in the wiki but would appreciate being shown, with examples, what everything means and how it's calculated.
Thanks
Nige
Being particularly thick myself, I'll have a go at putting it in the Noddy speak I understand, but to show worked examples involving the square root sign is a little tricky. To show the formulas I had to make a graphic in a vector program and export as a bitmap.
But here goes ...
(http://www.biopowered.co.uk/w/images/2/21/Jamesrlformula.png)
Fr equals the pump flow rate, so with a TAM that's 40 litres/min. So stick 40 in the formula in place of Fr. Next step is to work out the sum in the brackets (sort of mathematical rule because every thing in the brackets is just one item). so the brackets become 40 divided by 60 which is 0.6666. Having done that sum and reduced the bracket to a single number, you can now ditch the brackets.
The top line now becomes 50 times 0.6666 (sort of another mathematical rule, two numbers next to each other means multiply).
So top line now becomes 33.33.
Not quite sure how deep to delve into Noddy speak, so I'll delve deep! The little symbol that looks like a truncated capital H under the line is Pi. It's a number which was worked out by someone just a bit cleverer than me and something that you will just have to take for granted 'cos I can't explain how it's worked out. It's a fraction that goes on indefinitely, but for what we want 3.142 will be fine.
So under the tick thing you now have 33.33 above the line and 3.142 below. The line means divide, so the sum is 33.33 divided by 3.142 which is 10.6078
Now you just have one number, 10.6078 under the tick thing. The tick thing is a square root symbol and applies to everything under it. Easiest way to work this out is on a calculator with a square root symbol or just bang "square root 10.6078" into Google. This gives 3.2569. having done the square root you can forget about the tick thing.
So you're left with 2 times 3.2569 which is 6.51. This is the size of the throat in mm.
For 60 litres/min it works out at 7.876
Using the other formula, it's simply the square root of the flow rate. So for 40 litres/min it's 6.324mm and for 60 litres/min it's 7.745mm, so very little difference between the two sets of answers, but the latter is much easer to use.
Hope that A) is correct, and B) made sense!
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In response:
A) I hope so
B) yes it did...thank you.
Nige
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If, on the other hand, you take my simplified version of:
(http://www.biopowered.co.uk/w/images/4/45/Therecklessengineerformula.png)
For a flow rate of 60lpm, just take the square root of 60. Which is 7.75 - so your throat diameter would be 7.75mm
There's only 0.12mm difference which I count as negligible.
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I did say that right at the end and agree your formula is far preferable due to it's simplicity!
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James...how would your formula relate to eductors and stacked eductors?
Nige
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Apologies Julian - I didn't read that bit!
Not sure Nigel. All I've done is manipulate Jim's formula using algebra. I'm not sure how it relates to eductor design - but I'll think about it.
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Just goes to show the importance of keeping it as simple as possible.
Would it be worth adding a venturi calculator too? (I know I've not finished the cone one yet, it will happen!)
I didn't add one before because I figured the formula alone was enough but by the sound of it, it would be useful to have one. And we could potentially add eductor jet size to that as well.
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I'd go for it. The object of the site is to provide info and assist people. I'm happy to do new diagrams if required, just let me know.
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I've added the venturi calculator here:
http://www.biopowered.co.uk/forum/tools/throat.php
(Also in menu above).
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OK think I've got it now:
http://www.biopowered.co.uk/forum/tools/cone.php
Will verify the maths later (javascript is in radians so it's possible I've made a conversion mistake somewhere).
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Looks good. I can do a couple of graphics to explain the terminology, one for the input and one for the output. Can they be inserted in the boxes on the righthand side?
What about the hole in the top for the fitting? Similar calculation to the main OD I assume.
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Graphics could be inserted either to the left or right of the params/results section. I was thinking that for the time being we could just insert James' hand drawn diagram.
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Probably better if I modify the two top diagrams here ... http://www.biopowered.co.uk/wiki/Cone_bottoms_for_tanks
Just need to know what you are going to call the fitting cutout diameter.
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fitting cutout diameter
That works. Lets use it!
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Just modifying them now.
Would it be more useful to give the cone height rather than the flat cone diameter?
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First diagram here ... http://www.biopowered.co.uk/wiki/File:Cone_diagram_1.png
Let me know if it's a suitable size. I know it can be re-sized, but that will effect the text.
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Second one's uploaded ... http://www.biopowered.co.uk/wiki/File:Cone_diagram_2.png
Very much like the idea of offering the chord dimension, saves people measuring angles.
I've gone with radiuses instead if diameters as that's what people will be using to construct the cone.
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Nice one Julian, I've added both those, obviously some tweaking will be needed.
Regarding angle vs height, you anticipate that these should both be input parameters (the user choses which one they want to use and the other is updated automatically?)
Edit: done those changes
Maybe needs the fitting diameter added to the top diagram for clarity?
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Good work with the calculator, think the height bit is a big bonus. But I think the layout with the graphics could do with improving and the text has come out different sizes. Strange, because it the same text, exported at the same size.
How about I redo the second graphic to be two pairs, one above the other. That way you can shunt the graphics off to the right which will, I think, stop the page looking so cramped.
Also for consistency and clarity, I'll letter the remaining dimensions and angles. I'll not use Greek for he angles, just lower case (makes it easy if not quite correct)
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Are they any better?
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Just noticed you've added volume too ... brilliant!
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I think I've got that right but can't see on my laptop screen as it's so tiny!
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No, got it wrong! graphics are now positioned under the input and result boxes.
It'll be the naughty step soon!
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Allright, got it on the left, what thinketh you?
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Honestly?
Wellllllll ... Ummmm ... errrrrrr ... it's like this ... I ... errrr .... don't want to put a damper on things ... but ... errrrrrr .... if the truth be known ... and not beating about the bush .... and I really don't want to fall out over this .... but ...
Pants!
Try sticking the graphics over to the far right and the calc on the left with normal spacing ... keeps it step with all the other calculators.
Just one additional point ... if you click on the "Tools" button in the menu, you get a blank page.
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Yar, I thought you might say that, primary because it does indeed look pants. I'll see what I can do with it tomorrow.
This evening has been spent getting two heavy drums of Meth out of the car, vacuuming it and cleaning WVO stains off, then noticing the nail protruding from the flat rear tyre and swapping tyres. Darned cars.
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Well I think that's the limit of my html skills right there, I think we'd need someone that could do css to improve on that.
Having a page for the tools menu directly is something I can do however.
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Looks much better. I'm not an expert by any means, but the graphics and fields look to be in a table. Is it possible to justify the graphics cells to the right and normalise the fields cells for spacing?
This seems to work, graphics wise, having dumped the html into a very old copy of FrontPage ...
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<p>Calculate cone dimensions for fitting cone to drum.</p>
<form action name="ConeCalc">
<fieldset>
<legend>Parameters</legend>
<table frame="void" cellspacing="5" width="1031">
<tr>
<td width="233">Drum diameter (D)</td>
<td width="206"><input id="drumDiameter" value="572" onchange="CalcConeResults()" type="text" size="20">
mm</td>
<td rowspan="4" align="right" width="556"><img src="http://www.biopowered.co.uk/w/images/5/5e/Cone_diagram_1.png"></td>
</tr>
<tr>
<td width="233">Desired cone height (H)</td>
<td width="206"><input id="coneHeight" value="Enable javascript" onchange="CalcConeAngle()" type="text" size="20">
mm</td>
</tr>
<tr>
<td width="233">Desired cone angle from horizontal (a)</td>
<td width="206"><input id="coneAngle" value="30" onchange="CalcConeHeight()" type="text" size="20">
degrees</td>
</tr>
<tr>
<td width="233">Port fitting diameter (FD)</td>
<td width="206"><input id="fittingDiameter" value="22" onchange="CalcConeResults()" type="text" size="20">
mm</td>
</tr>
</table>
</fieldset><fieldset>
<legend>Results</legend>
<table frame="void" cellspacing="5" width="1031">
<tr>
<td width="230">Cone flat radius (R)</td>
<td width="203"><input id="coneLength" value="Enable javascript" readonly="readonly" onclick="document.ConeCalc.setstring.focus();document.ConeCalc.setstring.select();" type="text" size="20">
mm</td>
<td rowspan="6" width="562" align="right"><img src="http://www.biopowered.co.uk/w/images/e/ec/Cone_diagram_2.png"></td>
</tr>
<tr>
<td width="230">Cone flat diameter</td>
<td width="203"><input id="coneDiameter" value="Enable javascript" readonly="readonly" onclick="document.ConeCalc.setstring.focus();document.ConeCalc.setstring.select();" type="text" size="20">
mm</td>
</tr>
<tr>
<td width="230">Fitting cutout radius (FR)</td>
<td width="203"><input id="cutoutFittingRadius" value="----" readonly="readonly" onclick="document.ConeCalc.setstring.focus();document.ConeCalc.setstring.select();" type="text" size="20">
mm</td>
</tr>
<tr>
<td width="230">Cutout angle (b)</td>
<td width="203"><input id="cutoutAngle" value="Enable javascript" readonly="readonly" onclick="document.ConeCalc.setstring.focus();document.ConeCalc.setstring.select();" type="text" size="20">
degrees</td>
</tr>
<tr>
<td width="230">Cutout chord (C)</td>
<td width="203"><input id="cutoutChord" value="Enable javascript" readonly="readonly" onclick="document.ConeCalc.setstring.focus();document.ConeCalc.setstring.select();" type="text" size="20">
mm</td>
</tr>
<tr>
<td width="230">Cone volume</td>
<td width="203"><input id="coneVol" value="Enable javascript" readonly="readonly" onclick="document.ConeCalc.setstring.focus();document.ConeCalc.setstring.select();" type="text" size="20">
litres</td>
</tr>
</table>
</fieldset>
</form>
<p> </p>
</div>
</div>
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All I did was make the graphics cells 100% in size and justified right. The others I made specific widths to suit. Not sure about the vertical spacing of the fields. Would they all need to go into one cell to get round the spacing issue?
Don't know if any f that helps?
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Thanks Julian, I've taken that code, tweaked the values to nice round numbers and made it a little thinner - it's looking good!
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Looking good.
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jamesrl has taken a peer at it too just to verify that it all stacks up and he was most impressed with it.
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And rightly so! Think you've done a cracking job.
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Err - team effort!
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Appart from the brain power which went into each bit!
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Just one additional point ... if you click on the "Tools" button in the menu, you get a blank page.
Not any more - I've been refreshing my php coding skills and now it auto-generates a page linking to all the tools. :)