Author Topic: Talking Thermodynamics  (Read 154540 times)

Offline MJM460

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Re: Talking Thermodynamics
« Reply #90 on: June 22, 2017, 12:10:08 PM »
The Oval Diagram

Back to continuing to work through the oval diagram which was attached to my earlier post.

For an engine with no exhaust lap, the edge of the exhaust port is the horizontal line at the valve mid or zero position.  Exhaust lap would show as two horizontal lines, positioned above and below the centre point by the amount of exhaust lap.  We can see the exhaust valve closes a bit before piston top dead centre to give some compression, and opens before bottom dead centre for release.  All as expected. 

The angle of advance for this diagram had to be selected as 30 deg, to make the lap required match my measured valve equal to the valve displacement at piston dead centre.  This suggests my measured lap is really too big and I need to modify the valve ends.  On the other hand, for a simple mill engine, the diagram shows early cut off to give some expansion, and the exhaust valve closes to give some compression so it could be quite efficient for an engine with no reversing gear.

If you want to draw this diagram for your engine, start with the crank angles, then calculate the eccentric rotation as the crank rotation plus 90 degrees plus the advance angle.  It is also helpful to remember that the trigonometric ratios assume that an angle increases anticlockwise.  After that, simple trigonometry, a formula to increase the crank angle by some set amount for each row, and copy your formulae down until you reach one revolution, and use the graphing function of your spreadsheet.  However Dan and Zephryrin have provided links to web sites where the maths is already done, and use of these facilities is a good way to understand your valve setting.

In summary I am now satisfied that the traditional recommendation of no exhaust lap is a very good place to start, and in addition I now have a logical method to analyse the effect of changes in lap on either inlet or exhaust side.  But I still go back to my CAD method to check the width of the bars between the ports, and to make sure that the passages are clear and open.  No more glazed eyes.

So much for a slide valve, it all looks good when analysed according to our theory.  But what about my little oscillator?  I will look at that next time.

Thanks for following along.

MJM460
The more I learn, the more I find that I still have to learn!

Offline Dan Rowe

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Re: Talking Thermodynamics
« Reply #91 on: June 22, 2017, 07:08:13 PM »
MJ,
I found the rectangular diagram, it is also known as the harmonic diagram and the sine diagram. It is very similar to the oval diagram only the valve motion and the piston motion are separate curves and not combined as in the oval diagram.

The other three diagrams Zeuner, Reuleaux, and Bilgram, are for a different purpose entirely. They are all graphical constructions used to calculate the relationship between the geometry of the common D slide valve. They all give the same answer. The reason to use one over the other is really personal preference. The slide valve variable that these three diagrams are used to calculate are: valve travel, angle of advance, steam lap, exhaust lap, lead, cutoff, release, compression, and admission.

Obviously to start a slide valve design at least 4 of the above variables have to be known. The Zeuner diagram program by Dockstader has slider inputs for valve travel, cutoff, lead, and exhaust lap. The rest of the variables are calculated and displayed as changes are made to the inputs. I find this a very cumbersome because I have a lot of Shay locomotive data
that includes the valve travel and the angle of advance. I also know the lead for Shay locomotives is 1/16". This information with a glance at the drawings for the steam lap and I can construct a Bilgram diagram. It would be simple to show how to draw a Bilgram diagram for the valve in this thread.

I was a marine engineer and I have a love of vertical steam engines with Stephenson reverse gear. The first time I saw a Shay I saw a marine engine that got lost in the woods and I had to know more. The study of valve design and Stephenson gear took me many years and quite a few times I thought I would never figure out the secrets of how to design Shay valve gear. Finally understanding Bilgram only led to a much harder challenge of understanding Stephenson reverse.

You mentioned not many textbooks cover the thermodynamics of steam engines, well steam engines were fairly well developed while thermodynamics was still in its infancy. I believe it was the need to understand the theory of steam engines that was the driving force behind the discipline of thermodynamics. The earliest book in my collection of steam engine design books that covers thermodynamics similar to what I had in college is The Steam-Engine Theory and Practice 1905 by William Ripper.

The Wright brothers flight at Kitty Hawk would not have been possible without the wind tunnel data they generated before the successful airplane design. They aerodynamic data they generated was the best in the world in 1902.
https://wright.nasa.gov/airplane/results.html

Dan
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Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #92 on: June 22, 2017, 09:03:48 PM »
A new question.......does it take the same amount of coal/heat to boil water in an enclosed boiler at the top of a mountain as it does at sea level ? If the boiler is filled at sea level and then taken up a mountain, any difference ?? etc etc etc.......So can you to test a boiler at any altitude ??

Online Jo

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Re: Talking Thermodynamics
« Reply #93 on: June 22, 2017, 10:01:32 PM »
Willy you need to define the question better: the boiling point of the water will change as a function of altitude as does the combustion efficiency of the fuel. To provide the same volume of steam at altitude you need a bigger boiler or you would need to compress the air going into the combustion chamber.

Jo
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Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #94 on: June 23, 2017, 01:55:53 AM »
Willy you need to define the question better: the boiling point of the water will change as a function of altitude as does the combustion efficiency of the fuel. To provide the same volume of steam at altitude you need a bigger boiler or you would need to compress the air going into the combustion chamber.

Jo
 
Thanks Jo , I am a complete novice when it comes to thermodynamics, but being an autodidact i like to find out about things. I do make and say completely wrong statements and then get told and informed about what is actually correct and then i learn stuff !! I am part of a few clubs and things and am always being advised as to what is actually going on ! !! However i still only know what i know. Sorry about this lengthy diatribe but i am a gemini so i have an excuse !!!! I like your work with all your models and wish i could be  more prolific with what i do......... :)

Offline MJM460

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Re: Talking Thermodynamics
« Reply #95 on: June 23, 2017, 05:26:38 AM »
Hi Dan,  I thought you might be a marine engineer.  I have the greatest respect for your profession.  When at sea, the safety of the ship and the lives of all who sail on her are dependent on your ability to keep the engine running.  In the middle of a vast ocean, there is no one nearby to call on for help.  My activities were essentially land based, and steam power meant a turbine, so I never had need to come to terms with valve gear.

I suspect that you and I together are in a small (elite?) group of people who, when asked if we have read the classics, cheerfully reply, "Of course", thinking they mean classical thermodynamics.  After all, is there anything else you would read?   I did not mean that there were no text books on thermodynamics, just that it is glaringly absent from the modelling press.

So sincerely, please consider a thread about your adventures in valve gear, from the Stevenson's to the Shay.  If I have difficulty understanding them, I am sure there will be many others.  I for one will certainly be following along.

Now, Willy and Jo,  between you, you have mentioned in two (now three) short posts, at least six fundamental questions, the very questions which I suspect are behind nearly all of the confusion in our  understanding of steam engines and the boilers which fire them. 

I am very glad you asked, as I think you have collectively eloquently put your fingers on the big issues which most were afraid to mention.  I will start with the issue of boiling of water and get back to coal and combustion efficiency a bit later.

The basic issues of boiling water at elevation are dependant on whether you are talking about water in an open saucepan or kettle (even with a lid), or a closed space such as a boiler.  If you are  a mountaineer, or even live in Denver or Mexico City, you will observe that water boils at less than 100 deg C (212 deg F), and this might cause problems making a cup of tea or boiling an egg, the typical early school science examples.  To understand this we need to understand a few basics.

First, if we have both vapour (steam) and liquid water in a closed container, the pressure of the water vapour is dependant on the temperature alone.  If things are not happening too fast, they are considered to be in equilibrium, the pressure is uniquely determined by the temperature, and can be looked up in any steam tables.  It is called the vapour pressure.  Hold that thought for a moment.

If we could look at a scale where we could see the molecules, we would see the molecules in the gas moving fast in all directions.  They are a relatively long way apart, and each barely affected by the others except when they collide.   Some hit the vessel wall and bounce back into the fray.  But some hit the surface of the water.  Of these, some will lose enough energy in the collisions with water molecules that they are unable to escape, and stay in the liquid. 

In the water, molecules are also in random motion, but a lot slower and the molecules are closer together.  This close, there are attraction forces that keep the molecules in close proximity so that water stays together.  Some molecules hit the walls and bounce back.  Some reach the liquid surface, but are unable to escape the attractive forces of the closely spaced water molecules.  But  of these, a few with higher than average energy actually escape and join the gas.

If the number entering is the same as the number leaving the liquid, we call this equilibrium.  If there are more molecules leaving, this is not equilibrium, the water must be warmer than the equilibrium temperature, and extra molecules in the gas make their presence felt as extra pressure.  With more pressure, more molecules will return to the liquid and a new equilibrium is soon reached at a higher temperature.

If we heat an equilibrium mixture of water and vapour, some of the water will evaporate, but the temperature will not change until all the water has turned to steam.  The heat that goes into evaporating the water without increasing its temperature is called latent heat, and provides the energy necessary to get the molecules up to a velocity which allows them to escape the attractive forces at liquid spacing.

Boiling occurs when we put in heat fast enough that the water starts expanding into steam below the water  surface.  The huge change of volume causes the vigorous bubbling we call boiling when the suddenly large bubbles of steam quickly rise to the surface.

Now all of this is always true as I have described.  But notice I have only talked about a closed container containing only water.  No mention of anything else.  The confusing bit, the part that explains your confusion arises when, in addition to water there is something else also present, in particular if the something else is air due to the loose lid on our kettle.  The presence of air actually changes nothing but our perception, but that is the root cause of our problem.

That is enough to absorb in one sitting, don't be surprised if it takes more than one reading.  Next time I will explain what happens when our container also contains air.  And that will explain the conundrum of elevation.

Thanks for bearing with me

MJM460
The more I learn, the more I find that I still have to learn!

Offline jadge

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Re: Talking Thermodynamics
« Reply #96 on: June 23, 2017, 07:49:55 AM »
The book "The Steam Engine and Other Heat Engines" by J Alfred Ewing covers steam engines, including turbines, from both a pragmatic and thermodynamic viewpoint, aimed at undergraduate level. First published in 1894 I have a paperback copy of the 4th edition, published in 1926. The paperback copy wa published in 2013 by Cambridge University Press, who also published the original editions. It is what I use as a basis for understanding the thermodynamics of steam engines.

Andrew

Offline Dan Rowe

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Re: Talking Thermodynamics
« Reply #97 on: June 23, 2017, 05:09:47 PM »
MJ and Andrew,
The book I mentioned by Ripper is the 4th edition. The main reason I mentioned it is the first edition of the book printed in 1899 was the first text to include a temperature-entropy chart. The introduction of the temperature-entropy chart was by Macfarlane Gray who read his paper at the meeting if the Institution of Mechanical Engineers in Paris July 1889.

As to starting a thread on Stephenson valve gear, I have one on the web already, unfortunately, it is behind a privacy screen on 7-8ths.info which is a 7/8" scale model RR forum. The good news is I have not built the Shay engine I did the study for and I will cover the topic here when I get to the engine.

I was on vacation for a few weeks and did not read some of this very carefully and I was not near my library. You determined that the usual steam pipe was too small for your design. The problem is the assumption of 2000 rpm. This is a very fast speed for a double acting engine. Most double acting steam engines are much slower. Locomotives run about 300 rpm and marine engines vary from about 120 rpm to around 750 rpm. The reason a double acting engine does not make a good choice for high rpm's is the piston pushes and pulls the con rod, if the bearings are not kept tight there will be a knock as the force changes direction. A single acting engine is much more suitable for high rpm's because the con rod force is always in the same direction. To get the same power out of a single acting engine compared to a double acting engine of the same bore and stroke, the single acting engine has to turn at twice the speed.

Dan
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Offline MJM460

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Re: Talking Thermodynamics
« Reply #98 on: June 24, 2017, 01:06:51 PM »
Effects of air in the kettle

Hi Dan, I am really looking forward to following your Shay build, together with your valve gear analysis.  I hope it is not to early to start preparing popcorn, or at least planting the corn seed. 

You are probably right about 2000 rpm being too fast for running my little engine.  This would lead to needing a higher volume of steam, and requiring larger steam pipes.  It was a measured speed, using a non- contacting digital tachometer.  However, the engine was running unloaded, and I would expect it to run much slower under load.  It was also a short stroke oscillating engine which may affect the desirable running speed as the piston speed was quite moderate.  I agree with you about the possibility knocking at the crank pin due to rod load reversal, but the main purpose of the post was to show a rational basis for selecting pipe sizes.  I have noticed people here have a fair idea of the speed they want to run their engines and as you suggest, it is generally much slower.  I hope eventually to build a suitable dynamometer, probably based on a generator to allow me to measure power output, and I will repeat all my tests.

Back to boiling water at elevation-

Last time, I described boiling in a closed vessel with only water, partly liquid, partly vapour in the vessel.  So what happens in our kettle when we also have air at the liquid surface?   I suggested that it changed only our perception, but on reflection, it might have been better to say it changes everything.  Essentially, the pressure is now fixed at the local atmospheric pressure, and as boiling temperature is a function of pressure alone, it varies with the local atmospheric pressure.

Suppose we are boiling our kettle for a cup of tea at the top of a mountain.  We have been told there might be a problem, so we have brought a thermometer, which we put in the kettle and find it starts boiling at 95 deg C.  In this case, the water surface is in contact with the atmosphere through the spout and also the little vent hole you will notice in the lid.  Even the little gaps due to the fit of the lid help, so the pressure at the liquid surface is tied directly to the local atmospheric pressure.

 We look in our handy pocket extract of the steam tables, and find the equilibrium vapour pressure at 95 deg C is only 84.55 kPa.  This means the water vapour pressure at the water surface is only 84.55 kPa, and as the vigorous boiling tends to displace any air from the immediate surface, there is no gas mixture at the liquid surface. Any excess pressure in the kettle is eliminated by leakage to atmosphere, carrying with it any air that was initially in the kettle.  Further away from the surface, we have a mixture of air and water, and we don't know how much of each.  Well away from our kettle, we would find the air pressure measured by our barometer, had we brought an absolute pressure barometer such as a Mercury column, is only 84.55 kPa(absolute) compared with an average around 101.3 at sea level, and it matches the pressure in the steam tables that corresponds with our boiling temperature. This corresponds to very roughly 1500 metres.  If we were on Mt Everest, the boiling pressure would be nearer 50 kPa, and the temperature only a little above 80 deg C.  That might make tea making quite problematic.

The variation pressure (and hence in boiling temperature) with altitude varies in a complex manner depending on the atmospheric temperature variation and the amount of water in the air due to humidity, in addition to  elevation, and not necessary to know for our current discussion.  Google will find you some good information on this if you are interested.  I picked 95 deg as a point available in my steam tables, just for an example.  In fact even in your kitchen at sea level, it is difficult to get water to boil at exactly 100 deg C, due to the variation in atmospheric pressure as the weather patterns pass by, so if you are calibrating your thermometer, you need to know the atmospheric pressure at your location and make adjustments.  Again not necessary for our current purpose.

So I answer to the original question, in an open kettle, the water boiling point depends on the atmospheric pressure which depends on altitude, but in our closed boiler with only water present and not in contact with the atmosphere, the elevation does not affect the absolute pressure at which water boils.

One of the issues with boiling water in an open kettle is that boiling is a very vigorous action that is the very opposite of the reversible process necessary to keep the liquid and vapour in equilibrium.  The rapid motion as the vapour bubbles rise to the surface sweeps away any air, so the vapour near the surface is essentially all water vapour.  In an open vessel, the pressure is fixed to atmospheric pressure.  This very departure from equilibrium introduces an asymmetry between boiling and condensing.  When we get to discuss condensers, you will see a very different and perhaps surprising effect of even an small amount of air.

I hope that helps to answer some of the questions.  Next time I will discuss how these concepts apply to boiler testing.

Thanks for following along.

MJM460

The more I learn, the more I find that I still have to learn!

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #99 on: June 24, 2017, 02:26:03 PM »
Thermometers....? If it is of the mercury type in a glass tube, is the 15Lb atmospheric pressure sort of squeezing the tube slightly.? at altitude is this squeezing less so the temperature would appear to read less ?? If the boiler is at altitude would this reduced pressure allow the tube to expand slightly ? Would the boudon tube in the pressure gauge also expand slightly thereby giving a different reading than at sea level ? or does everything cancel each other out ? Sorry to be so pedantic about this but as a novice it would be good to know how things actually behave !!

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #100 on: June 24, 2017, 02:35:20 PM »
In one of my electrically heated boilers there is a low water safety device that switches off the power. This is in the form of an insulated probe (PTFE) . When the water level drops below the end of the probe it switches off the 250Volts using a separate 9Volt battery circuit. I am surprised that as the boiler is full of steam, this wet steam does not complete the circuit. !! Is this going off at a completely separate tangent or is there some relevance to the topic in hand ??..............

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #101 on: June 24, 2017, 02:40:17 PM »
I have noticed that when you buy a new barometer from a shop, they actually calibrate it for you, Here in Norwich the local shop that sells them is 8 meters above sea level !!!..........Also as we know there is a standard  Meter ,Yard Kilogram etc etc so is there a standard i Bar , 15Lbs  somewhere ??or is this being a bit silly !!!!!
« Last Edit: June 24, 2017, 02:43:56 PM by steam guy willy »

Offline MJM460

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Re: Talking Thermodynamics
« Reply #102 on: June 25, 2017, 12:59:59 PM »
Hi Willy, you are in good form tonight, but no, they are not silly questions, and your aim of wanting to understand exactly how things work is why I am writing this thread.  It's just that you are asking questions faster than I can answer.  After all, for both of us, this is our hobby, not our full time occupation.

You are quite right observing that the glass thermometer is subject to external pressure and the inside is closed off from the outside.  So it is squeezed a little less at altitude.  But I emphasise the LITTLE less.  One atmosphere is very small compared with the strength if the thermometer tube under external pressure, so it does not have much effect.  I have not had cause previously to look up a stress strain curve for glass, but I would hazard a guess (and you know engineers are not comfortable with guesses), that the effect on diameter is so small that you would not be able to measure it with your standard workshop tools, and I am trying to stay practical.  If you are really worried, you could use instead a thermocouple, properly calibrated at sea level of course, for your temperature measurement.  I am sure any pressure effect could then be safely ignored.

You know when we only had slide rules for calculation, we had an advantage.  You could only read at best three significant figures, unless you had a monster slide rule, but there was a real limit to the accuracy you could obtain.  Surveyors used seven figure log tables, but for most engineering purposes three significant figures are enough.  Any more is only useful so you can get an exact balance of calculated results.  We used to dismiss small errors as slide rule errors, but there were times when this hid a real error due to an incorrect calculation.

Thermodynamic calculations often involve subtracting two large numbers for a small result.  It would be good to be able to measure temperature to better than 0.1 deg C, but that requires laboratory quality instruments that are not affordable for most, and not really required.  I am confident the error in your thermometer from 1 atmosphere change in pressure would be much less than 0.1 deg C.

So you are right in your understanding of what happens, but I believe the magnitude is small enough not to matter.

Your electric boiler level probe does not use a mechanical contact which opens or closes, but a conductivity probe which measures a change in resistance (which results in a change in a small current in a circuit,) so the range of possible readings is continuous or analogue, not binary.  It then uses an amplifier to lift the currents to a useful level, perhaps to operate a relay, which opens to shut off the mains voltage.  So it depends on the difference in conductivity between steam and water.  Again I do not know, or have immediate access to the data, but you could use your volt meter to measure the resistance of your probe first in cold water, then as you heat the boiler to boiling, then proceed to low level so you measure the steam resistance.

You need to be very safety conscious when you do this test.  Just disconnect your level controller from the probe for the entire test and do not open up the circuit with the mains power connections.  You are the safety switch, so watch the level gauge and switch off as soon as you make the necessary readings.  Also work assuming there could be a fault which allows your probe to touch the mains voltage in the heater element (even though it is most unlikely).  Use a 600 V insulated meter rated for mains use and proceed as you would if everything was at 240 V.  Don't take any risks, again this is only your hobby.  If you are not sure, don't do it, just take my word for it or research the operation of your probe from other sources.  I expect you don't need any of these warnings, but neither of us know who else is reading this, and what their state of understanding or the condition of their equipment might be.

The topic is only limited by what I am prepared to try and answer, based on my 40 years in an industry where this understanding was as basic as arithmetic to an accountant.  I am trying to pass a little of it on to where it might be helpful.  It gives you a fair bit of latitude on topics.

Definitely not being silly about units.  I had intended to get to it anyway, but now you have asked, this is how it works at a practical level.

Pressure is force per unit area, so it's measurement is based on force and area.

Force is defined by Newtons equation, F equals mass times acceleration.  Usually written F= ma

It is the unit which most distinguishes Imperial and ISO metric units, and which causes the most confusion in all calculations involving force.  Metric for a few lines, then I will explain that further.

Mass is measured in kilograms and we have a standard bar of some expensive exotic alloy for that.

Acceleration is defined as change of velocity per second, velocity and acceleration require only length and time for measurement, and we have standards for those.

Now a very powerful analysis technique for these problems is called dimensional analysis.  Don't run away, it simply relies on a principal that in a rational equation, each side of the equals sign has to have the same units.  In addition, each term that is added or subtracted must have the same units.

In plain language, you cannot add apples and pears, and apples cannot equal oranges.  Sounds simple but that principle is behind the equations for force and the scaling of wave generation when ships move through water and many other complex problems.

So if we define F=Ma, we are saying the units of F are the same as the units of m times a.

Let's do it.  I will use square brackets to mean "the dimensions of", just read it that way, then

[F] = [m] times [a]. Then continue with [m] = kg,  and [a] = m/s^2. Read s^2 as seconds squared or
s raised to the power of 2.

So [F] = kg times meters divided by seconds squared.  Or more conveniently [F] = kg.m/s^2

The metric unit of force was given the name Newton and the symbol N, so 1 Newton = 1 kg.m^2.

Not so hard was it?  You only need mass length and time for these measurements.

You might say what about kilogram force?  Now, Wash your mouth out, that is not an ISO unit.  It is a hangover from the same issue as that curse of students everywhere, the pound force.  There was a time when people did not understand the difference between mass and force (has much changed?). Force was given the units of pound, the same as the unit of mass, and both combine in the term weight.  You can see the confusion.  People have tried to extract themselves from this by introducing either the small unit of force, the poundal, or the large unit of mass, the slug.  Personally I don't like either of them.  Alternatively they introduce a constant g, being the same value as the agreed standard acceleration due to gravity, but when to include it asks the student.  So metric for me.  The constant is nearly always one.  But I understand the issues of converting workshop tooling and material dimensions.

Now we have units of force, kg.m/s^2, we can move back to pressure.

Pressure is force per unit area.  Area is length squared, and we have a standard for length.  We have a standard for mass, and one for time, so we standards for all the dimensions we need to measure pressure.  There is no need for a standard bar.

I hope that answers the questions at least sufficient for the moment, it's getting late.

Happy reading

MJM460

Ps forgot the bourdon tube, oh well, next time.
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Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #103 on: June 25, 2017, 01:31:59 PM »
Thanks for this, getting a bit clearer.......you mention the Poundal and also the Slug  never heard of that, but, hopefully getting rid of all the slugs on my allotment will be a weight off my mind !! Between the 9 volt battery connection circuit and the 250 volt mains circuit there is a light sensitive IC so it should be quite safe exploring relative resistances with my 1960's AVO or would a modern digital instrument be better ?........also as you are in the antipodes does the water go down the plug hole anticlockwise...the correolis effect ? Or is this another urban myth ?
« Last Edit: June 25, 2017, 01:38:01 PM by steam guy willy »

Offline MJM460

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Re: Talking Thermodynamics
« Reply #104 on: June 26, 2017, 08:36:48 AM »
A little more on pressure measurement.

Hi Willy, I am glad this is making things a little clearer, but sounds like it needs more work.

I realised, after sleeping on it, that I had stopped a bit early on the pressure standard, so a little more to complete the trail from the mass, length and time standards to the units for pressure.

The unit of pressure, Newton per square meter, or N/m^2, was given the name Pascal.  Now this is a very small unit, so we usually use kiloPascal, or kPa, and you will realise that 1 kPa = 1000 Pa.

To help you appreciate just how small, atmospheric pressure, around 14.7 psi is 101.3 kPa, or
101300 Pa.  Mind you for a candle powered Stirling engine, the Pascal would be a very convenient unit.

I should also correct my statement about the pound force.  I found an appropriate reference and there was a standard pound force, defined as the force exerted by a one pound mass due to gravity.  It was complex to use, to eliminate the effect of the air displaced by the mass and so on.  When it was applied to Newtons law, which basically says F is proportional to mass times acceleration, it was found that the proportionality constant could not be 1, but had to have a value equal to the gravitational acceleration.  So the equation in imperial units had to become F = ma/g, and that constant, g, has plagued students ever since.  As the value of g varies at different points on the earth and with elevation, a standard value, agreed at 32.174, is used for the value of the constant.

The principals of dimensional analysis can not be avoided, so the constant also had to have units to make the equation dimensionally correct.  A little maths and you will see the units must be
 lbm.ft/(lbf.s^2).  Quite an awkward mouthful, but necessary to maintain the distinction between force and mass.  In addition, it violates two desirable features of a good standard unit.  First, in a fundamental equation such as F is proportional to m times a, the preferred constant is 1, and second if a constant is required, it should be dimensionless, meaning it has no units.  However the use of g with the applicable units was necessary to accommodate the traditional use of pound as a unit for weight.  Slugs are best fed with snail bait, or fed to birds, but not both.

You can see the beauty of the ISO system.  In Newtons equation, the constant is unity, and it is dimensionless, the equation becomes F = ma and with this equation we can easily deduce the units for force without an additional reference standard.  The resulting unit of Force, the kg.m/s^2, is given the name Newton.  When we apply this to pressure we get Newton per square meter.

I had intended to talk about your question about the bourdon tube.  We had better get M. Bourdon's name spelt correctly or we will have Marv chiding us, ever so gently of course.

You might have noticed in another thread, that one of our forum members is actually making his own pressure gauges, and started with a finite element analysis of the curved tube that forms the basis of the instrument.   Oh, to have had access to that software earlier in my career!  Even access now.  It is a thread well worth following.  I thought it was a bit too much like watch making for my eyes and fingers, but on closer reading, I find it involves more watch breaking. 

I can't do that finite element analysis, but I do have a good feeling for piping.  So I will put on my piping engineers hat, and see how we go.  Now, the Bourdon tube is very like a pipe if you recognise that it is nearly all bend and not much straight.  Also, it has a closed end, and is flattened  a bit, so that its cross section is oval rather than round, but it is still just a pipe and a pipe is something I understand.  So what do we get from this.  First a pipe is designed to hold pressure, and the strength required is determined by the difference between the inside and outside pressure and the diameter. If the inside pressure is higher, the stress-strain relationship for the material means it increases in cross sectional area.  If the higher pressure is outside, it decreases. 

There is also longitudinal stretching under pressure.  When the pipe is bent, the longitudinal dimension change has a very interesting effect.  The bend tends to open up a bit.  The cross section also tends to flatten a bit towards an oval shape.  If it has already been flattened a bit, the change in curvature will be even  greater.  It might surprise you that this happens, and can be easily measured, even on a 12" diameter pipe with 1/2 " thick steel walls, if you apply enough pressure.  Of course the little Bourdon tube is thinner and smaller and the straightening is a lot more noticeable.  The closed end is linked by levers and a gear to the needle so the movement is even more visible.  The scale is marked zero at the needle location when the tube is open to the atmosphere (same pressure inside and outside).  It can move either way from this zero point depending on whether the pressure being measured is greater or less than atmospheric, and the scale is calibrated accordingly. 

The important point in regard to your question, is that the straightening of the tube is due to the stress in the metal, and the radii of the  longitudinal bend and the cross section al radius, not dependant on volume contained in the tube.  Remember, the tube is open to the space whose pressure you are measuring, so any change in volume on results in a very small movement of fluid into or out of the tube.  Any volume effect is already reflected in the scale calibration.

Next time I hope to get back to the questions remaining from you and Jo's earlier comments.

Thank you for helping make this more of a conversation, with your questions.

MJM460

PS - your Avo meter will be fine.  I assumed an optoisolator in your circuit, but you have to disconnect your circuit to make an accurate resistance measurement.  Plug hole circulation is urban myth, Coriolis is real, but plumbing detail has more effect.  If you take notice you should also see different plug holes, sometimes CW, sometimes CCW rotation.  You also have Coriolis in the northern hemisphere!
« Last Edit: June 26, 2017, 08:44:08 AM by MJM460 »
The more I learn, the more I find that I still have to learn!