Viscometers.
The proper place for making measurements of viscosity that are to be used in evaluating non-dimensional groups is in a physics laboratory using primary methods. This would not be done in the normal day-to-day business of engineering.
The main fluids that are moved about by engineers are probably water, oil, beer and milk in that order and water and oil dominate. The movement of oil is the one that causes the engineer to become involved with viscosity. The oil that is extracted from the Earth’s crust varies in its composition. It is made up of all sorts of inflammable compounds of hydrogen and carbon and, when they are separated, some are heavy and thick and some are light and runny and everything between. For use in motor-cars, whether petrol or diesel, crude oil is refined and the light fractions separated to become petrol or light diesel[1]. What is left after distillation is inflammable and therefore a fuel. It will still contain a mix of different compounds some of which are not very desirable in flue gas. It is also thick stodgy stuff that needs careful management if it is to be burnt in power stations or ships. It is also typical of tar oils.
The main problems for engineers can be illustrated by that of burning heavy oil in power stations. There the oil has to be kept hot enough to flow into pumps to shift it into and out of tankers whether they are road tankers or sea tankers and also for the rest of its journey to the boilers. Once delivered to storage tanks on site it must be kept warm usually by steam heating and then pumped through burners in the boilers. These burners atomise the oil, that is, they produce a continuous spray of finely divided oil that must evaporate before it can burn. The flame is so hot that, it can only be viewed through welding goggles, but even so it can be stratified by the different temperatures at which the several fractions evaporate. Burning this oil so that the combustion products are least harmful and the combustion most efficient needs careful control of the flame by controlling the inlet conditions to the burner. Atomisation depends on the high pressure at the burner, the mobility of the oil and I suppose other properties of the oil like film strength and surface tension. It is not just about viscosity and even if it were to be there is still the problem of its composition of many fractions. I think that the flame is mainly monitored by just looking at it.
From the above it is clear that engineers want to know about the state of the oil as it goes through its various stages before burning and, whilst it might be interesting to have an accurate value for the variation of the viscosity of the oil with temperature, some hands-on method of finding a working value of viscosity is much more desirable at the final point of injection at the burner. There are various viscometers available and I can make a assessment of their suitability for engineering use.
The Ostwald viscometer
I must start with the Ostwald viscometer because it is the one that might just escape from the laboratory. The following (In blue.) is what I wrote for a laboratory exercise for students in 1984. I make no apologies about including it because it tells us how empirical sciences grow. I have no time to bring it up to date and, for my purpose, it would be pointless.
British Standard 188:1977
This standard is the latest (In 1984.) in a series that have been published in 1923, 1929, 1937, 1957, and now 1977. and the original reason for the publication was to encourage the use of CGS units of viscosity rather than the arbitrary units such as Redwood seconds and Saybolt seconds.
The standard introduced by the BSI is shown in figure 6-5 with its standardised dimensions.
In 1957 there was a range of 8 viscometers to measure the viscosities of most liquids. However between 1957 and 1977 manufacturers of viscometers produced their own ranges with detailed differences in design and, in 1977 BSI removed the length constraints and approved commercial designs.
In 1977 BSI changed to SI units of viscosity and also introduced a new definition for coefficient of viscosity and introduced ideas of shear stress and rate of shear to take the concept of viscosity as a property a further step away from Newton’s concept.
The standard lays down test procedures for measurement of viscosity and these are more suited to a physics laboratory than to a power station.
The standard says “ the principle of the test is the measurement of the time taken for a reproducible volume of liquid to flow through a capillary viscometer under an accurately reproducible head and at a closely controlled temperature. The kinematic viscosity ( ) is then calculated from the measured flow time and the calibration factor of the viscometer.”
In use a viscometer is filled with the test sample to just above level G. It is then mounted in a bath of water that is gently stirred and heated under the control of an accurate thermostat. When the temperature is steady at some desired value the level of the sample is adjusted to be at G by extracting some of the sample. The sample is then sucked up tube 2 until the level is above E. Then the time is taken for the level to fall from E to F.
Then the kinematic viscosity is found from an expression of the form:-
where is the elapsed time and and are calibration constants.
Look on the internet and you will see that BSI have not displaced Redwood seconds and Saybolt seconds as practical measurements of viscosity for use by engineers. In my experience the BSI instrument is bound to fail. Their viscometer is much more a device for use in a laboratory and once it goes into a lab bureaucratic paperwork and procedural delays make it useless for the engineer who could well have a whole tank full of oil to burn efficiently in a boiler now, not in a month’s time. Redwood viscometers and Saybolt viscometers have been reworked to make them more “user-friendly” and are still very much in use.
It is hard to see where BSI was going when it sought to alter the definition of viscosity. But the mindset of BSI is that of the physicist and not that of the engineer just as the NPL was when SI was introduced. They seem not to be interested in how engineers, or anyone else for that matter, go about their work.
The Redwood viscometer.
In the late nineteenth century three secondary viscometers came to prominence, the Redwood viscometer in Great Britain, the Saybolt viscometer in America and the Engler viscometer in Europe. They all depended on the same method of performing a “time-of-discharge” test on a sample where the time depended on laminar flow through a short pipe.
The sample of oil to be tested is held in a pot that is filled to a set point and, when the temperature of the sample is at some desired value, the sample is allowed to drain from the pot through the short pipe until a set volume has drained away. The kinematic viscosity, if that is what is measured, is calculated from the elapsed time for the draining.
The
Redwood viscometer was made[2]
by Sir Boverton Redwood in about 1880. I looked for an authentic drawing of a
Redwood viscometer but the important details seem to have changed in with
successive re-drafting for textbooks. Lewitt’s book of 1943 shows in figure 6-6
the design of the viscometer as it was somewhere between 1923 and 1943 and I am
inclined to think that this is correct. I give a copy of Lewitt’s diagram in
figure 6-6 and I have drawn the essential central pot to a larger scale in
figure 6-7. The brass pot that has a height of about 90mm or 3.5² and an internal diameter
of 46.5mm, that is, the inside diameter
of 2² tubing having a 14 swg
wall thickness. The bottom of the pot is clearly a turned insert. The
all-important feature is the agate insert. It has a bore of 1/16² or 1.62mm and is 1/2² or 12.5 mm long. This is an
Imperial size but it was a volume of 50 cc that was allowed to drain out.[3]
The unlikely detail is the creation of a spherical seat at entry to the pipe so
that it might be sealed with a ball on the end of a wire. I think that we would
avoid this shape of entry to the pipe nowadays. The pot is fitted with a hook
gauge to give an accurate position for the upper surface of the sample before
carrying out the test. The level drops by 30mm during the test to drain away
50cc of the sample. This is measured with the small graduated flask under the
hole.
The pot is surrounded by a water bath that is electrically heated by coils round the bath. The water is manually stirred with the paddles round the pot. Thermometers in the sample and in the water permit the adjustment of temperature. The test is started by lifting the ball off its seat but I do not know where it is placed during the test, perhaps it just rests in the groove in the base plate. Wherever it goes its position is part of the test procedure. The Redwood viscometer is still in regular use as are the others and I need to offer reasons for this to be the case.
There can be no dispute about the fact that if you carry out the same test with the same oil in identical equipment you will get the same result.[4] This means that, if you want to buy fuel for a power station and a supplier offers the 10,000 tons you need with a Redwood number, when tested at a set temperature, of say 1,200 seconds and you know that your equipment can burn fuel with this Redwood number, there is no physical reason not to buy if the price is agreeable to you both. The seller knows that when the fuel arrives you can test a sample long before very much of it has entered your storage tanks. Here we have the legal and practical basis for a transaction. Nowhere in this is viscosity even mentioned, only the Redwood seconds because, in the end, the final adjustment that ensures that the fuel is burnt as well as possible is all about looking at the flame just as a plumber does to adjust his gas torch. The Redwood viscometer that makes this transaction possible is a simple piece of equipment that is very suited to the task for which it was designed and this is why it, and the other two viscometers, will go on being used. There are two versions of this viscometer and the second is designed for heavy oils.
The Redwood viscometer is capable of being reproduced very accurately and however much one might question the use of a ball with its spherical seat that produces such an unlikely entry to the short pipe it cannot be changed now and there is no undisputed case to do so.
So what does the Redwood viscometer actually measure?
If the energy equation is applied to the viscometer at some instant during a test when the difference in level between the free surface and the exit from the short pipe is we get:-
.As and are both atmospheric pressure, is zero and = , this reduces to
.
The loss is the friction lost in laminar flow in the short pipe. There is little option but to use the Pouseuille expression and put:-
The loss between 1 and 2 where and are the diameter and length of the short pipe, and are the viscosity and density of the sample. Then:-
This expression tells us that the Redwood viscometer will only work if the kinetic energy is very small when compared with the loss in the pipe. So, if the expression is reduced to
we can examine it.
First it can be rearranged to give where is a constant that can be calculated from the dimensions of the viscometer and .
Now, in a short time a volume of the sample will flow from the viscometer and cause a drop in level of where are the diameters of the pipe and the pot.
Substituting for and re-arranging we get:-
which can be integrated between 0 and T and the start and finish values of h. The result of this is that the time for 50 cc of sample to drain from the pot is given by T = a constant .
So the Redwood viscometer does not give us a value for the viscosity but for which crops up so often that it is given a special name, the kinematic viscosity and denoted . It now has units of metres2/second where it used to have units of centistokes with units of centimetres2 /second. To change from centistokes to SI units divide by 10,000.
So the Redwood viscometer has the potential to measure kinematic viscosity but, of course, it all depends on whether we were justified in using the Pouseuille expression to relate the time of discharge and the kinematic viscosity. We cannot know from argument but it is evident that the pipe is too short for the shape at entry to have no effect so we must turn to the actual performance of the viscometer.
In graph 6-1 I have plotted the performance of a Redwood number 1 viscometer when tested using fluids of known viscosity at 21°C. I think that most engineers would be delighted to have any basic data with this sort of accuracy. The graphs for the viscometer at 60°C and 93°C show little more error.
I was trained to denigrate these secondary viscometers as being very poor compared with U tube viscometers. I regret passing this view on to others when lecturing. This text gives me a chance to offer a more reasoned view.
Other viscometers
Stokes showed that the force exerted on a sphere moving with laminar flow of fluid round it can be given by where .
If ball, e.g. a steel bearing ball, falls freely through a liquid that is expansive compared with the size of the ball it will reach its terminal velocity and if that velocity is measured the value of the viscosity can be deduced from it. This is the principle of the falling ball viscometer.
There is a case for continuously monitoring the viscosity of fuel oil just before it enters the burners of a boiler. It could then become part of an automatic control system. Then a cylinder rotating inside a sleeve would give a suitable element to form part of a transducer. It could be a rotating disc.
There used to be a falling ball viscometer that was really portable. It was in two parts, a steel ball about 1² in diameter and a steel cup attached to a handle. The cup had the same radius as the ball but it had three high spots that created a small clearance between the ball and cup when one was fitted inside the other. In use the ball was immersed in a sample of oil and the cup, on its handle, was placed over the ball under the oil and left for the ball and cup to come into contact when sufficient oil had been squeezed out. The clearance was then full of oil. The viscometer was then lifted and the time taken for the ball to fall out of the cup was measured to give a useful estimate of the viscosity.