Talking Thermodynamics

[steam guy willy]

Hi thanks for all this info , and i'm glad i don't have to pay the full rate for these consultancy fees !!! . I have noticed when using propane bottles in the summer that you do get a frost line forming at the level of the liquid  when using the gas at full tilt ! I shall do another boiler test with the extra insulation. These videos were done 8 and 10 years ago so are not of the quality and ease that we can do today on my Apple computer !! .

[MJM460]

On boiling propane -

Hi Willy, just to complete yesterday's question on the way the ends are placed.  The inspector has to take into considerations the issue that get presented and I am sure that after a while the most common and troublesome problems are well known.  I would expect that the inspectors talk to each other and compare notes about the design that are people are more likely to present correctly.  If I understand the issue addressed in the code, it is to verify that the silver solder has flowed right through the joint as well as that the flange is the correct length.  I guess with those 5.5 mm cameras mentioned in another thread, inspecting the penetration on the inside is a bit easier, but the measurement is not.  Has to be measured before soldering.  I don't really know.  However the issue of heat loss is easy to control as with the flange facing outwards it is pretty easy to apply as much insulation as you need to minimise the heat loss.  So I would talk to the inspector about the design, present all the prepared parts before soldering, and go along with the instructions given, and insulate the end result (after the hydrostatic and steaming tests are approved).  Your outside cladding then determines the visible appearance of the boiler.

The propane in your gas bottle behaves very like the water in your boiler, but the equilibrium pressure and temperature are just in a different range.  At atmospheric pressure, propane boils at minus 42 deg C.  At 20 degrees, it's equilibrium pressure is about 700 kPa(g), or 100 psig.  When you open your fuel valve to burn some gas, the pressure drops as has leaves the bottle.  This means the gas and liquid are no longer in equilibrium.  The vapour pressure of the liquid is then higher than the gas pressure.  Some liquid has to be boiled off to maintain the equilibrium.  Now we don't generally put a flame under the gas bottle, so we only have the heat available in the liquid and from the atmospheric air.  The temperature difference is initially zero, so no heat transfer from air and the heat comes from the liquid which rapidly cools.  Now with a large enough bottle surface area and pleasant temperatures like we enjoy here, say 20 degrees or more, and a low fuel off take, you may soon get enough heat transfer to maintain the new low pressure.  But the liquid will be cooler than it was when the gas valve was closed.  Turn up the burner a bit, and the liquid temperature soon falls below the dew point of the atmospheric air, and moisture condenses on the outside of the bottle.  If the propane pressure falls to around 350 kPa(g), the temperature will be around zero and any further drop in pressure soon causes that moisture to freeze, as you have seen.  Much more likely in your climate where you spend much more time below 20 than above.  However in Canada, and many US states a different story, and low ambient temperatures can be insufficient to maintain the gas burner pressure requirement.  The propane itself does not freeze at these temperatures.

With butane, the pressures are quite a bit lower, so in cool climates, some exhaust steam heat, or even just conduction through a common base plate with the boiler is used to maintain the pressure in the small gas bottles generally used in models.  I can give you the butane pressures if you need them.

It's not really about consulting fees, it is a pleasure and a privilege to contribute something back to the forum where I learn so much, and my machining skills have a long way to go.  It is just useful information for many aspects of our modelling hobby, not well known within the model making community, but was basic to my work throughout my career.  It is not secret information, just basic thermodynamics.  I am delighted that you are finding it interesting, and many others obviously keep coming back despite my often wordy style.

Thanks for looking in

MJM460

[steam guy willy]

hi <Thanks for that... I was looking at a refrigeration van today and when the chap opens the door a whole lot of white swirling mist appeared. Can you/ explain what i was actually seeing it looked a bit like steam but obviously not ? !! Thanks for the info about the rock wool and i shall pack it as tight as possible............Willy

[MJM460]

Hi Willy, that type of question is always a little tricky to answer because there are so many contradictory intuitive thoughts about the process involved.  The way I work it out is like this.  The air in the refrigerated van is cool compared with the atmospheric air outside.  Hence when the door is opened, and the cooler, more dense air flows out and is warmed when it mixes with the outside air.  In the process the warm air is cooled.  Now if it happens to be fairly high humidity, it can be cooled below the dew point temperature, the temperature at which the humidity becomes 100%, and if cooled further, excess moisture must condense.  The moisture is well mixed with the air so condenses in tiny droplets.  These appear as a mist, like a fog or a cloud.  So what you saw was a fog of moisture condensed out of the outside air by the cool air from the van.  The tiny droplets are so small that viscous effects in the air prevent them from quickly falling into a continuous liquid phase, and they remain suspended for quite a while.  Eventually the overwhelming quantity of the warmer outside air evaporates the droplets and so the fog does not spread far.

It is often said that warm air can hold more moisture than cold air, which is a reasonable enough observation.  However it can also be looked at in terms of partial pressure.  You can look at the steam tables and see that at low temperature, the equilibrium pressure is lower.  If the water vapour partial pressure in the air reaches that equilibrium pressure, it cannot increase further and any excess results in some condensation.  This point in an air mixture is described as 100% relative humidity.  If there is less moisture in the air, so the partial pressure of the water is less than the equilibrium pressure for that temperature, we use the term humidity, or relative humidity, which is defined as the percentage of the equilibrium pressure of the moisture in air.

When you look at this way, you can easily see that if you have air with a certain moisture content, and you then cool it, then the same absolute moisture content becomes closer to the equilibrium pressure at the lower temperature.  So the humidity becomes higher and eventually if you continue cooling the air, it reaches equilibrium pressure for the new air temperature, and condensation starts as you saw at the back of the van.

I hope that dispels the mystery of the fog at the van, which is the same process as the formation of  fog on a chilly morning, or of a cloud high in the sky, and of the visible steam from a kettle or from your engine exhaust.  Water vapour itself does not reflect light and is quite invisible.

Just a short post tonight, a short night as we start daylight savings, so must put the clocks forward, after a big family day today.

Thanks for looking in,

MJM460

[Kim]

OK, so now it's my turn to ask a question, that came out of your answer to Willy here.

What exactly IS steam?  Steam is water in gaseous form, right?  We just happened to give it a special name. In fact we gave water is so special, it got 3 names, one for each form (Ice, water, steam - where as most things only get one name and you have to specify form "Liquid Natural Gas" for example).  But my question: how is 'steam' different than water suspended in air?

At standard atmospheric pressure, the water has to be at 100C to become steam.  So, I can see that the water vapor hovering around the door of the refrigeration truck couldn't be steam, because it is clearly not 100C.   But then what makes water vapor different from steam? Is it just the amount of energy contained in the individual water molecule?  Is that the only difference?  Is Humidity NOT water in gaseous form?  What is humidity then?

Thank you for all the interesting discussion MJM.  I did take a term of Thermodynamics in school, and I'm following most of what your saying, but clearly, making that head learning mesh with the real world is challenging me.

Kim

[steam guy willy]

Hi Kim ,good questions there and would it be possible to answer  using words of two syllables or less ?!! And to add to this ....if you had water in a sealed tank and forced air at high pressure into it what would happen ??

[paul gough]

Taking a step back to horsepowers and specifically boiler horsepower. Re-reading 'Perfecting the American Steam Locomotive' by J Parker Lamb, in Chapter 3, 'The Physics of Steam Power, p. 43, he gives the equation; boiler horse power (maximum) = 1/6 grate area (sq ft) X boiler pressure (psi). He states this is an approximate value and an empirical formula. I presume it was used as a comparative figure by designers, maybe a guide to match boiler capacity to maximum demand of certain size cylinders and a means of estimating fuel consumption. Were there any other uses for the resultant? Was it just a designers 'rule of thumb'? Anyone have any more on this??? Regards, Paul Gough.

[MJM460]

More on humidity -

Hi Kim, always glad to have more questions.  I think you are right on the mark pointing out that water is so special.  After all it is a basic necessity for life, at least life as we know it.  Only three words for water says something about the climate where you live.  I believe that the Eskimos have around thirty names for snow.  As a sometimes skier, I can describe about six, but thirty is amazing.  I suspect that is the heart of the dilemma.  We knew about water, ice and steam long before we knew anything about thermodynamics, so we had words for the different forms we knew, long before we had the need for more specific terms, or even knowledge to explain our observations.

To get to the basics, first the term water, defines the chemical compound consisting of two hydrogen atoms and one oxygen in each molecule, what ever its form.  But the term obviously overlaps common usage for the liquid.  We know it exists in three forms, usually known as phases, solid, liquid and gas, as do many other compounds.  And we tend to use the word steam for the gas phase, but perhaps more particularly when we can see it, like near the spout of a boiling kettle.  And sometimes we use the word vapour.  But it is not so well understood that the gas phase does not reflect light and cannot be seen, like very close the the spout of the kettle, and the mist we see a small distance from the spout is in fact fine droplets of condensed liquid.  Same as a morning fog, sea fog or even thin cloud.

I had to resort to the dictionary to check some of the normal usage definitions.  It says steam is water in the form of a gas or vapour, or water changed to this form by boiling, and extensively used for mechanical power or for heating purposes.  Also the mist which forms when when gas or vapour from boiling water condenses in air.  It also defines steam point as the equilibrium temperature of liquid and vapour phases of water at 101.315 kPa which is equal to 100 degrees C.

So it seems that you are correct in associating the word steam with boiling, and in answer to your question about the difference between steam and the water suspended in air as fog etc. I suggest it is tied to the method of generation of that form in common usage, but the first clause in the dictionary definition just says water in the form of gas or vapour, followed by the word or.

Applying thermodynamics and our knowledge of how the equilibrium pressure of the liquid and gas phases of water change with temperature, I suggest that there is no physical difference.

That leads to the question of humidity.  I suggest this is our everyday description of the moisture content normally found in air.  Normally, moisture content of air, which is proportional to the partial pressure of water vapour in the air, is not at the equilibrium pressure for the prevailing atmospheric temperature, but always less.  The weather bureau records relative humidity which is the percentage of the equilibrium pressure at that temperature.  This means that the actual moisture content of the air varies with temperature, when at the same relative humidity.    As I mentioned yesterday, the steam tables tell us the equilibrium pressure for each temperature.  The relative humidity reading tells us the proportion of that equilibrium pressure which is actually present.  It is then clear that if air with a certain partial pressure of water vapour is cooled, then eventually a temperature is reached where that partial pressure does equal the equilibrium pressure, so condensation must begin if cooling continues.

I have every sympathy for your feeling of challenge in applying the basic thermodynamics you learned.  I went into a career where it was a basic tool used every day, but while I realised that the knowledge had the answer to everyday questions, some of Willy's questions have really got me thinking carefully to make sure I had an answer that was properly supported by the theory.  I still check very carefully for relevant examples in my textbook before I post on some of the more obscure ones.

Hi Willy, I think I failed on the request for words of no more than two syllables, but I hope the longer words are generally well enough known that you won't need a dictionary to read it.  I should have mentioned yesterday, that when that condensation begins, the heat released helps warm the cooler air so the condensation soon stops, hence the limited extent of the mist.  But the new question, you have a boiler for example with water as a liquid, plus some vapour, at the equilibrium pressure for the temperature once the system has settled and all the temperatures are equal, plus some air to make a total pressure of atmospheric pressure prior to sealing the boiler.  If you now use a compressor to add more air, you increase the partial pressure of the air, but not the water vapour.  If you are extremely pedantic, you have to make sure the air is cooled to atmospheric temperature before it enters the boiler, otherwise it will just need more time to be at true equilibrium.

Some of the air will dissolve in the liquid phase, a quite small amount, and the rest just adds to the total pressure in the boiler.  You didn't say how high was high.  You boiler probably is designed for something around 100 psig when cold, or 700 kPag.  At this sort of pressure, the air in the vapour space and the water vapour act near enough to independently, as described by Dalton's law of partial pressures.  If you have a suitable vessel and suitable compressor, the situation is probably about the same at 500 psig.  You could continue to 5000 psig.  I had to specify a compressor for that once, and you don't want to go that far, but somewhere around that stage, perhaps lower or even higher, the atoms in the vapour space do get sufficiently crowded to affect each other and you can no longer simply add the partial pressure.  I am not very familiar with working in that range, and I am not sure just where it starts to be important.  Then, when you release the pressure, the amount dissolved can no longer be accommodated, and the excess dissolved air bubbles out like an opened can of soft drink.

Hi Paul, I can see that boiler horse power is still fascinating you.   As you have said, the term and also the formula are just empirical guidelines, and the formula is not dimensionally consistent unless that constant, 1/6, has the right units.  It is not just a pure number.  However there is some sense to the form of the formula, as grate area is probably a good indicator of the amount of coal that can be burned in a given time, and hence energy input per unit of time. And we know that pressure is necessary for the steam to do work.  So it makes sense that if you make a graph of potential engine brake horsepower against grate area times pressure, you might get some sort of correlation.  Especially in the days before super heaters.  Not necessarily linear, though a straight line can always be drawn as an approximation.  But whether the 1/6 factor is appropriate I really don't know.   To avoid variation due to the engine efficiency, you could use the output of that ideal adiabatic engine to make the results a bit more consistent.  Probably no help to you in designing your little locomotive boilers, but a bit of interesting history.

Thanks to everyone for looking in

MJM460

[paul gough]

Thanks for your comments on the boiler horsepower issue. I have always been fascinated by the goings on in boilers, particularly loco boilers with their high steaming rates and the relatively tight space they have to occupy. I am hoping that at some point our thermo discussions might flow toward and into the 'what is happening' from fire hole door to stack top. Almost none of us are combustion or chemical engineers but some grasp of underlying principles regarding what is required for a successful boiler and the combustion that goes on in it might expand our understanding and avoid misconceptions and advance design.

 One specific question I have and have not been able to find any satisfactory answer to is; do the boundary layers scale down, with steam, air, products of combustion remain more ore less a constant dimension from full size to model dimensions and is there any significant change in this 'dimensioning' when the fluid is relatively static, eg. in a vessel, or when moving at some velocity, such as steam in a pipe that is vented or flue gases in fire tubes, (leaving aside here 'disruption' such as by steam bubbles in the water adjacent to a heating surface)? Finally, if there is dimensional variability, what parameters might impact, eg. pressure, temperature, velocity, the proportion of the vessel eg. does the boundary layer in a 5mm  copper steam pipe differ from one  50mm in dia. or a 12 mm fire tube compared to a 50mm one? Also does the material matter, by this I mean is a higher conductance metal like copper have different boundary layer formation than that adjacent to a steel tube? Hope all this is not too headache inducing! Regards, Paul Gough.

[MJM460]

Boundary layers and scaling -

Hi Paul, obviously you are talking about scaling of size, and not that boiler scale that grows in our boilers if the water contains various impurities.  And you allude to the fact that the gas composition and properties are the same in our models as in full size, and how that might affect our models.

Most of the research work in fluid mechanics is done on scale models and much thought goes into how to address this very problem.  We don't have many,if any at all, cases where we can find a suitable fluid to use in a model that has scale density and viscosity in particular.  Dimensional analysis is one of the techniques used to uncover various combinations of properties that are dimensionless so experimental results can apply to all sizes.  For example the length of a pipe divided by its diameter is dimensionless, so an experiment can be done with a certain size and length of pipe and the results are found to apply to another pipe diameter if the length is such that the ratio of length to diameter is the same.  One example is the development of a velocity profile in a pipe.  At the entrance to the pipe, the flow velocity is roughly uniform across the circular cross section of the pipe.  However, the fluid velocity in contact with the pipe wall tends to be zero.  In low flow situations, the flow proceeds along the pipe, viscosity means the stationary layer at the wall slows the layer immediately inside and so on until a roughly parabolic profile develops where the velocity on the centre line is about twice the average velocity calculated from the flow through the pipe and the cross sectional area.  This profile develops fully at a length where the L/D ratio is in the range of 60, though it varies with the actual velocity.  At higher flow rates, the flow becomes turbulent, the profile is a bit more of a flat topped parabola, which is fully developed at L/D in the range 25 - 40.  Unfortunately when applied to the diameters in our models, the lengths are equal or perhaps longer than our model, so we generally operate in the range of the developing profile.  Another of those dimensionless groups, given the name Reynolds number after the one who identified it, involves viscosity, density, velocity and diameter in a dimensionless combination.  Knowing those properties do form a dimensionless combination you can work it out yourself with a little trial and error.  Then, while you cannot find corresponding "scale fluids", if you run your experiment at equal Reynolds numbers of your model and full size, many results will correlate nicely.  So Reynolds number effectively replaces velocity and compensates for viscosity, diameter and density as well.  Of course with a ship model, there is wave making to consider, but there another dimensionless group called the Froude number, will allow you to calculate a speed for your model that will make the same wave pattern as the full size ship at its appropriate speed.  But fundamentally the flow in a model boiler tube of a certain l/d can be accurately compared with the flow in a full size boiler tube of the same l/d.  One of the two must be determined by experiment, then the other can be calculated.  Of course in fluid mechanics experiments, every effort is taken to stick to the issue of flow and avoid other energy transfer.  Mostly because the properties of viscosity and even density are quite temperature sensitive.  It is hard enough to understand what is happening in the boundary between the stationary wall and the bulk fluid with steady properties, without having to deal with changing viscosity and density as well.  And the reverse applies, the velocity affects the effective temperature profile.  If the velocity is high, warmed fluid is carried on quickly and replaced by cooler fluid so the temperature gradient is effectively changed, and that changes the viscosity which changes the velocity profile.  Not to hard to get a headache in that area, and probably not very useful to go much further. 

The take away points are first, the velocity in a pipe is zero at the wall and increases towards the centre to give a roughly parabolic velocity profile, perhaps a bit flattened in the centre, and that large and small sizes can be compared provided that size and velocity at the comparison points have certain dimensionless combinations of properties controlled to be equal in the sizes being compared.

The other point you alluded to is the effect of the velocity of a fluid on the heat transfer rate.  It is worth noting that velocity has a huge impact, mostly because of its effect on the temperature gradient near the wall, and this temperature gradient plus conductivity of the fluid are the main factors influencing the film coefficient which determines the overall heat transfer rate.  It is sufficiently important that there are two distinct types of convection heat transfer recognised.  First there is natural convection, where the velocity is determined only by the change in fluid density due to the heat transfer.  Second, there is forced convection, where the fluid is given additional velocity, perhaps by a fan or a pump.

You could look at the coffee cooling experiment, perhaps tea so we don't yet have to talk about the effect of froth on the surface.  If you just let the cup sit, the tea is warmer than the air, so liquid and vapour are not in equilibrium at the surface.  Some tea evaporates to cool the air and increase the vapour pressure at the surface towards equilibrium.  However, this also warms the air near the surface, which decreases in density, and warm air rises to be replaced by more cool air.  This is called evaporative cooling, and occurs in a cooling tower, a coolgardie safe, or an evaporative air conditioner.  Similarly, there is heat transfer through the sides of the cup as we know because the cup feels hot, so it does loose heat to the air, but slower than the surface as China is not a very good conductor.  Never the less, it is an example of natural convection.  Eventually the tea cools to a drinkable temperature and we normally avoid continuing the experiment until the tea is at air temperature.  That would not only be wasteful of the tea, but also of or time, as the nearer the tea gets to air temperature, the slower the heat transfer goes, proportional to temperature difference, remember?

Now if you blow on the surface of the tea, you remove that extra vapour, so the surface is no nearer equilibrium and the evaporation and evaporative cooling rate continue at a higher rate.  Similarly blowing cool air on the sides of the cup carries away the warmed air, replacing it with cooler air, so the effective temperature gradient is greater and the cooling proceeds faster, unless of course you are a politician!  That is called forced convection.  The increase in cooling rate is not linear with velocity, so the complexity continues if you are trying to analyse the situation.  But a fan would supply more air at a higher velocity than blowing, so does further increase the cooling rate, and shortens the time to cool.  Even so, as the temperature difference between the cup and the air decreases, the heat transfer rate slows.

The flow and boundary layer problems are discussed in any engineering fluid mechanics text book, they are pretty heavy reading but worth a look in a library.  The heat transfer is described in any engineering heat transfer text book, again very heavy reading, but definitely the place to go if you want to explore the issues further.

I hope that helps.  I think back to wet steam next time, but eventually we will get to the boiler, though I am limited in not being a combustion engineer, so any contributions will be welcome.  Oh, and I will talk about the effect of copper or steel properties on the heat transfer.

Thanks for following along,

MJM460

[steam guy willy]

Hi, interesting stuff again ....LBSC used to say that you cannot scale nature , so interesting to note that they do make models that then work when scaled up. On reading about combustion in boilers it was noted that air intake above the fire grate helped wth the compleat combustion of the gasses above the fire. also when burning wood in an open fire you never use a grate ,(this is what my mum use to say when we had open fireplaces in the house) !! I do have a book somewhere that talks about combustion produced by Charringtons a coal supplier but i don't know where that is at the moment...........

[paul gough]

Hi Willy, Air supply above the grate goes back a very long way, talking locos here, many of the large modern engines on the U.S. had air jets along the sides of fire boxes, most I think induced by steam, some compressed air, a few things brought about their re-application. Things had reached the limits inside a conventional firebox/combustion chamber due to enormous grate sizes of the big semi-articulated locos (Mallets) firebox volumes weren't sufficient for combustion, nor was turbulence or air fuel ratio of certain types of fuel, usually coal. The history of 'overtire jets' as they are commonly called was an interesting line of research I did a few years ago and it leads back to very early locos in Britain. There were penalties for 'smoke nuisance' and all sorts of things were tried, including 'air tubes', at this time they were at the front of the firebox, just tubes secured through the outer and inner wrappers of the firebox, later more tubes in rows and different positions some with steam jets were tried out. About the time when locomotives transitioned to burning coal rather than coke it was found that larger firebox volumes and the invention of the 'blower' to induce more draught, especially when stationary, overcame the 'smoke problem' sufficiently for the extra boiler making of 'tubes' and maintenance to override any gain, but of course the Super Power era of locos in the U.S. caused things to go full circle so to speak.

Hi MJM, thanks for the detailed comments. They go some way in explaining conditions and to the improvement in steaming of a couple of boilers, loco type, that I 'played with'. The gas fired one had a boiler excessively long and the coal fired one had fire tubes too small, thus amounting to the same thing. Introducing thin strips of metal plate twisted into a low amplitude spiral the same width as the tube dia. brought about better steaming in both boilers. The gas fired one transitioned to thin stainless strips as a permanent fix but the 12" gauge coal burner was a failure in that the strips became impossible to remove to clean the tubes due to being cemented in by the soot or burnt out. We deduced that more turbulence and slower velocity of the gases contributed to better heat transfer. Seems it wasn't far wrong.

One question please: Does the friction in small steam supply pipes to an engine you spoke of previously, 1/8" Dia I think, come from friction between the 'stationary' boundary layer and the main body of fluid or from turbulence caused by the high velocities induced by the small pipe, if both, is one dominant?? I'm  not clear on this.  Regards Paul Gough.

[MJM460]

More on scaling models -

Hi Willy,  we always had open fires when we were young, some had a grate, some not.  A good fire can be made in either.  I just checked with my wife who is a real expert fire maker, a result of her farming background, and she also has no preference for grate or no grate.  Air over the top is helpful in making sure combustion is complete, you don't want the possibility of carbon monoxide entering the room as it is very toxic, unlike carbon dioxide.  There are a few other nasties in the partially burnt fuel, depending on just what you are burning, so a good idea to introduce some excess air.   But you also need air into the seat of the fire to support combustion.  A fire needs to be compact enough to generate a high enough temperature to exceed the required temperature for combustion of wood, and needs enough air for combustion but not enough to cool the fire and extinguish it.  In burner technology, these two air sources are called primary air and secondary air.  I always thought the grate was useful in small fireplaces to help prevent burning wood rolling out, not so necessary in a larger one where it is easier to build the fire so it is quite stable.  There will be something behind your mothers advice, there usually is, but I am not sure that I understand the real reason.  I wonder if anyone else has more detail.

Hi Paul, Thanks for the interesting information on secondary air in locomotives.  I probably signed off a bit prematurely last night, not time wise of course, but there is probably some value in following the topic a little further.x

The Reynolds number is density x velocity x diameter / viscosity.  The units for density, velocity and diameter are well known, though perhaps I should emphasise the unit for diameter is metres, not mm.  The units for viscosity are Newton seconds per metre.  You can easily check that it is dimensionless.  That formula emphasises the place of density and viscosity.  Tables often list kinematic viscosity instead of absolute viscosity, but kinematic viscosity = viscosity / density, so it can easily be used in the formula as that ratio is directly in the formula.  Kinematic viscosity has the units L^2/T.  If you have a larger tube and a smaller one, and you operate both at the same Reynolds number for equal flow patterns, viscosity and density will be the same for both, so you can see there is an inverse relationship between velocity and diameter between a smaller and a larger tube.  Now  dimensional analysis tells you that you need a quantity with the dimensions length, so a representative size.  It does not tell you what that length should be.   You might be aware that our aeronautical colleagues use the wing cord in calculating Reynolds number,  not the span, while in piping, using diameter as the representative size yields better correlations than using length when the experiments are analysed.

Another relevant dimensionless number is the ratio of cross sectional area to surface area of a tube.  Cross sectional area is important to the flow rate through the tube for a given pressure drop,  while the surface area is important to heat transfer.  For problems involving heat transfer and flow, you can't get the same conditions in both tubes for both flow and heat transfer, but some investigation might lead to an optimum diameter, where larger does not have enough surface area, and smaller does not allow enough flow.  And of course you need enough pressure drop to drive the flow.  So just finding a dimensionless ratio does not mean you can use it to scale the design.  This example illustrates that our models are small boilers, not scaled down ones.  However when trying to model a prototype, we do use a constant length ratio for as much as possible so that the overall proportion and appearance is preserved.

Those spirals are an interesting technique.  I am not sure whether they just provide extra surface area to absorb heat then transfer it to the tube wall by conduction where it contacts, or whether they modify the flow pattern so improving convection heat transfer.  Or more likely it is a complex combination of both possibly plus other factors.

The definition of friction factor uses only the wall shear stress and V^2/2g.  There is another term, apparent shear stress, which varies across the radius of the pipe.  The variation is due to the effect of turbulence and momentum transfer, but the momentum transfer requires a transverse component of velocity.  Obviously must be zero at the wall, but increases as you move into the bulk flow where the flow is turbulent.  The apparent shear stress appears to be linear between the wall and the centre, so near the wall viscous effects predominate, then moving inwards, the two become equal, then momentum transfer and turbulent effects predominate.  I will be interested to see how you use this, but again there is more detail in any engineering fluid mechanics text.  The maths gets pretty heavy quickly and I am definitely less comfortable in this area.  I hope that is sufficient for now.

Still planning to return to wet steam next time,

MJM460

[paul gough]

Again, thanks for the leads into the goings on in pipes, I really hope I have not caused any of this threads devotees to run away because of my fluid dynamics enquiries. I think I have enough grasp of things now to know what to look for when I get the chance to pursue some combustion and fluid flow tomes. I'll have to take a trip down to J.C.U. library, I think they teach some of the M.Eng. undergrad program in Cairns, so maybe I'll find a few books there. For the moment I'll retreat to my cell, meditate on your discourses and take a vow of silence, lest our followers become restive at my abstruse questions. Regards, Paul Gough.

[Steam Haulage]

Hi MJM,

Could you please expand the definitions which you use in your 4th Paragraph regarding viscosity and density. I am especially interested in how you measure these values and the practical units of measurement in the various forms of apparatus used. I presume your work depends on treating water and steam/air mixtures as fluids.

Jerry