1-Viscosity

2-Viscometer

3-Relation Between Viscosity &Temperature

4-Vogel Equation

5-Programming Of Vogel Equation

1st

what is viscosity?

Viscosity • Viscosity is a measure of the resistance of a fluid to deform under

shear stress. It is commonly perceived as "thickness", or resistance to flow. Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. Thus, water is "thin", having a lower viscosity, while vegetable oil is "thick" having a higher viscosity. All real fluids (except super fluids) have some resistance to shear stress, but a fluid which has no resistance to shear stress is known as an ideal fluid or in viscid fluid (Symon 1971).

• When looking at a value for viscosity the number that one most often sees is the coefficients of viscosity, simply put this is the ratio between the pressure exerted on the surface of a fluid, in the lateral or horizontal direction, to the change in velocity of the fluid as you move down in the fluid (this is what is referred to as a speed gradient). For example water has a viscosity of 1.0 x 10-3 Pa∙s and motor oil has a viscosity of 250 x 10-3 Pa∙s. (Serway 1996, p. 440)

Newton's theory

• Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to shear. The force required for this action is a measure of the fluid's viscosity. This type of flow is known as a Couette flow.

• Laminar shear, the non-linear gradient, is a result of the geometry the fluid is flowing through (e.g. a pipe).

• In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force.

• Isaac Newton postulated that, for straight, parallel and uniform flow, the shear stress, τ, between layers is proportional to the velocity gradient, ∂u/∂y, in the direction perpendicular to the layers, in other words, the relative motion of the layers.

• Here, the constant η is known as the coefficient of viscosity, the viscosity, or the dynamic viscosity. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity.

• The relationship between the shear stress and the velocity gradient can also be obtained by considering two plates closely spaced apart at a distance y, and separated by a homogeneous substance. Assuming that the plates are very large, with a large area A, such that edge effects may be ignored, and that the lower plate is fixed, let a force F be applied to the upper plate. If this force causes the substance between the plates to undergo shear flow (as opposed to just shearing elastically until the shear stress in the substance balances the applied force), the substance is called a fluid. The applied force is proportional to the area and velocity of the plate and inversely proportional to the distance between the plates. Combining these three relations results in the equation F = η(Au/y), where η is the proportionality factor called the absolute viscosity (with units Pa·s = kg/(m·s) or slugs/(ft·s)). The absolute viscosity is also known as the dynamic viscosity, and is often shortened to simply viscosity. The equation can be expressed in terms of shear stress; τ = F/A = η(u/y). The rate of shear deformation is u / y and can be also written as a shear velocity, du/dy. Hence, through this method, the relation between the shear stress and the velocity gradient can be obtained.

• In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterised by the fluid density ρ. This ratio is characterised by the kinematic viscosity, defined as follows:

• James Clerk Maxwell called viscosity fugitive elasticity because of the analogy that elastic deformation opposes shear stress in solids, while in viscous fluids, shear stress is opposed by rate of deformation.

Units • Viscosity (dynamic/absolute viscosity): η or μ• The IUPAC symbol for viscosity is the Greek symbol eta (η), and dynamic viscosity is

also commonly referred to using the Greek symbol mu (μ). The SI physical unit of dynamic viscosity is the pascal-second (Pa·s), which is identical to 1 kg·m−1·s−1. If a fluid with a viscosity of one Pa·s is placed between two plates, and one plate is pushed sideways with a shear stress of one pascal, it moves a distance equal to the thickness of the layer between the plates in one second. The name poiseuille (Pl) was proposed for this unit (after Jean Louis Marie Poiseuille who formulated Poiseuille's law of viscous flow), but not accepted internationally. Care must be taken in not confusing the poiseuille with the poise named after the same person!

• The cgs physical unit for dynamic viscosity is the poise[1] (P; IPA: [pwaz])) named after Jean Louis Marie Poiseuille. It is more commonly expressed, particularly in ASTM standards, as centipoise (cP). The centipoise is commonly used because water has a viscosity of 1.0020 cP (at 20 °C; the closeness to one is a convenient coincidence).

• 1 P = 1 g·cm−1·s−1 • The relation between Poise and Pascal-second is:

• 10 P = 1 kg·m−1·s−1 = 1 Pa·s • 1 cP = 0.001 Pa·s = 1 mPa·s

Kinematic viscosity: • Kinematic viscosity (Greek symbol: ν) has SI units (m2·s−1). The cgs physical

unit for kinematic viscosity is the stokes (abbreviated S or St), named after George Gabriel Stokes. It is sometimes expressed in terms of centistokes (cS or cSt). In U.S. usage, stoke is sometimes used as the singular form.

• 1 stokes = 100 centistokes = 1 cm2·s−1 = 0.0001 m2·s−1. • 1 centistokes = 1 mm²/s

• Dynamic versus kinematic viscosity• Conversion between kinematic and dynamic viscosity, is given by νρ = η. Note

that the parameters must be given in SI units not in P, cP or St.

• For example, if ν = 1 St (=0.0001 m2·s-1) and ρ = 1000 kg·m-3 then η = νρ = 0.1 kg·m−1·s−1 = 0.1 Pa·s [1].

• For a plot of kinematic viscosity of air as a function of absolute temperature, see James Ierardi's Fire Protection Engineering Site

Molecular origins • The viscosity of a system is determined by how

molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green-Kubo relations for the linear shear viscosity or the Transient Time Correlation Function expressions derived by Evans and Morriss in 1985. Although these expressions are each exact in order to calculate the viscosity of a dense fluid, using these relations requires the use of molecular dynamics computer simulation.

Gases

• Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. The kinetic theory of gases allows accurate prediction of the behaviour of gaseous viscosity, in particular that, within the regime where the theory is applicable:

• Viscosity is independent of pressure; and • Viscosity increases as temperature increases.

Liquids • In liquids, the additional forces between molecules become

important. This leads to an additional contribution to the shear stress though the exact mechanics of this are still controversial.[citation needed] Thus, in liquids:

• Viscosity is independent of pressure (except at very high pressure); and

• Viscosity tends to fall as temperature increases (for example, water viscosity goes from 1.79 cP to 0.28 cP in the temperature range from 0 °C to 100 °C); see temperature dependence of liquid viscosity for more details.

• The dynamic viscosities of liquids are typically several orders of magnitude higher than dynamic viscosities of gases.

Viscosity of materials

• The viscosity of air and water are by far the two most important materials for aviation aerodynamics and shipping fluid dynamics. Temperature plays the main role in determining viscosity.

Viscosity of air

• The viscosity of air depends mostly on the temperature. At 15.0 °C, the viscosity of air is 1.78 × 10−5 kg/(m·s). You can get the viscosity of air as a function of altitude from the eXtreme High Altitude Calculator

Viscosity of various materials

• The Sutherland's formula can be used to derive the dynamic viscosity as a function of the temperature:

• where:• η = viscosity in (Pa·s) at input

temperature T • η0 = reference viscosity in (Pa·s) at

reference temperature T0 • T = input temperature in kelvin • T0 = reference temperature in kelvin • C = Sutherland's constant

Can solids have a viscosity ?

• If on the basis that all solids flow to a small extent in response to shear stress then yes, substances know as Amorphous solids, such as glass, may be considered to have viscosity. This has led some to the view that solids are simply liquids with a very high viscosity, typically greater than 1012 Pa•s. This position is often adopted by supporters of the widely held misconception that glass flow can be observed in old buildings. This distortion is more likely the result of glass making process rather than the viscosity of glass.

• However, others argue that solids are, in general, elastic for small stresses while fluids are not. Even if solids flow at higher stresses, they are characterized by their low-stress behavior. Viscosity may be an appropriate characteristic for solids in a plastic regime. The situation becomes somewhat confused as the term viscosity is sometimes used for solid materials, for example Maxwell materials, to describe the relationship between stress and the rate of change of strain, rather than rate of shear.

• These distinctions may be largely resolved by considering the constitutive equations of the material in question, which take into account both its viscous and elastic behaviors. Materials for which both their viscosity and their elasticity are important in a particular range of deformation and deformation rate are called viscoelastic. In geology, earth materials that exhibit viscous deformation at least three times greater than their elastic deformation are sometimes called rheids.

• One example of solids flowing which has been observed since 1930 is the Pitch drop experiment.

Bulk viscosity • The trace of the stress tensor is often

identified with the negative-one-third of the thermodynamic pressure:

• which only depends upon the equilibrium state potentials like temperature and density (equation of state). In general, the trace of the stress tensor is the sum of thermodynamic pressure contribution plus another contribution which is proportional to the divergence of the velocity field. This constant of proportionality is called the bulk viscosity.

Eddy viscosity

• In the study of turbulence in fluids, a common practical strategy for calculation is to ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an eddy viscosity that characterizes the transport and dissipation of energy in the smaller-scale flow. Values of eddy viscosity used in modeling ocean circulation may be from 5x104 to 106 Pa·s depending upon the resolution of the numerical grid.

Fluidity • The reciprocal of viscosity is fluidity, usually symbolized by φ = 1 / η or

F = 1 / η, depending on the convention used, measured in reciprocal poise (cm·s·g-1), sometimes called the rhe. Fluidity is seldom used in engineering practice.

• The concept of fluidity can be used to determine the viscosity of an ideal solution. For two components a and b, the fluidity when a and b are mixed is

• which is only slightly simpler than the equivalent equation in terms of viscosity:

• where χa and χb is the mole fraction of component a and b respectively, and ηa and ηb are the components pure viscosities.

The linear viscous stress tensor

• Viscous forces in a fluid are a function of the rate at which the fluid velocity is changing over distance. The velocity at any point is specified by the velocity field . The velocity at a small distance from point may be written as a Taylor series:

• Where is shorthand for the dyadic product of the del operator and the velocity:

Measuring viscosity • Viscosity is measured with various types of viscometer,

typically at 20 °C (standard state). For some fluids, it is a constant over a wide range of shear rates. The fluids without a constant viscosity are called Non-Newtonian fluids.

• In paint industries, viscosity is commonly measured with a Zahn cup, in which the efflux time is determined and given to customers. The efflux time can also be converted to kinematic viscosities (cSt) through the conversion equations.

• Also used in paint, a Stormer viscometer uses load-based rotation in order to determine viscosity. It uses units, Krebs units (KU), unique to this viscometer.

2nd

Viscometer

Viscometer

• A viscometer (also called viscosimeter) is an instrument used to measure the viscosity and flow parameters of a fluid.

• The classical method of measuring due to Stokes, consisted of measuring the time for a fluid to flow through a capillary tube. Refined by Cannon, Ubbelohde and others, the glass tube viscometer is still the master method for the standard determination of the viscosity of water. The viscosity of water is 0.890 mPa·s at 25 degrees Celsius, and 1.002 mPa·s at 20 degrees Celsius.

• Glass tube viscometers can have a reproducibility of 0.1% under ideal conditions, which means immersed in a fluid bath, but are not ideally suited for measuring fluids with high solids contents, or viscosity. Further, they are impossible to use to accurately characterise non-newtonian fluids, which the majority of fluids of interest tend to be. There are international standard methods for making measurements with a capillary instrument, such as ASTM D445.

Vibrating viscometers • These kinds of viscometers are the most rugged system to

measure viscosity in process condition. This technology is very simple, the active part of the sensor is a vibrating rod. The vibration amplitude varies according to the viscosity of the fluid in which the rod is immersed. These viscosity meters are suitable to measure clogging fluid and fluid very viscous (up 1 000 000 cP). Nowadays, all industrials around the world consider these viscometers as the most efficent system to measure viscosity. As a matter of fact the rotational viscometers required too much maintenance, can not measure clogging fluid, and after an intensive use the measurement is not stable and need a new calibration. The vibrating viscometers are the best because there are no weak parts, this process viscometer require no maintenance and the measurement is instantaneous and need not new calibration. This technology is patented by SOFRASER.

Rotation viscometers • Rotational viscometers uses the idea that the force required to turn an object

in a fluid, can indicate the viscosity of that fluid.

• The common Brookfield-type viscometer determines the required force for rotating a disk or bob in a fluid at known speed.

• 'Cup and bob' viscometers work by defining the exact volume of sample which is to be sheared within a test cell, the torque required to achieve a certain rotational speed is measured and plotted. There are two classical geometries in "cup and bob" viscometers, known as either the "Couette" or "Searle" systems - distinguished by whether the cup or bob rotates. The rotating cup is preferred in some cases, because it reduces the onset of Taylor vortices.

• 'Cone and Plate' viscometers use a cone of very shallow angle in bare contact with a flat plate. With this system the shear rate beneath the plate is constant to a modest degree of precision and deconvolution of a flow curve; a graph of shear stress (torque) against shear rate (angular velocity) yields the viscosity in a straightforward manner.

Stormer viscometer • The Stormer viscometer is a rotation instrument used to

determine the viscosity of paints, commonly used in paint industries. It consists of a paddle-type rotor that is spun by an internal motor, submerged into a cylinder of viscous substance. The rotor speed can be adjusted by changing the amount of load supplied onto the rotor. For example, in one brand of viscometers, pushing the level upwards decreases the load and speed, downwards increases the load and speed.

• The viscosity can be found by adjusting the load until the rotation velocity is 200 rotations/minute. By examining the load applied and comparing tables found on ASTM D 562, one can find the viscosity in Krebs units (KU), unique only to the Stormer type viscometer.

• This method is intended for paints applied by brush or roller.

Miscellaneous viscometer types

• Other viscometer types use bubbles, balls or other objects. Viscometers that can measure fluids with high viscosity or molten polymers are usually called rheometers or plastometers.

• Vibrational viscometers date back to the 1950s Bendix instrument, which is of a class that operates by measuring the damping of an oscillating electromechanical resonator immersed in a fluid whose viscosity is to be determined. The resonator generally oscillates in torsion or transversely (as a cantilever beam or tuning fork). The higher the viscosity, the larger the damping imposed on the resonator. The resonator's damping may be measured by one of several methods:

• 1-Measuring the power input necessary to keep the oscillator vibrating at a constant amplitude. The higher the viscosity, the more power is needed to maintain the amplitude of oscillation.

• 2-Measuring the decay time of the oscillation once the excitation is switched off. The higher the viscosity, the faster the signal decays.

• 3-Measuring the frequency of the resonator as a function of phase angle between excitation and response waveforms. The higher the viscosity, the larger the frequency change for a given phase change.

• The vibrational instrument also suffers from a lack of a defined shear field, which makes it unsuited to measuring the viscosity of a fluid whose flow behaviour is not known before hand.

• In the I.C.I "Oscar" viscometer, a sealed can of fluid was oscillated torsionally, and by clever measurement techniques it was possible to measure both viscosity and elasticity in the sample.

• Principle of the combined viscometer and densimeter.

• Density measurement principle.

• Viscosity measurement principle.

Computer Controlled Ubbelohde Viscometer

• For liquid viscosity measurements we have recently developed a computer controlled system around a commercial Ubbelohde viscosimeter (Schott KPG Ubbelohde viscometer). The viscometer is arranged in a double wall glas cylinder for thermostating with a commercial circulating thermostat. To pump the liquid in the capillary a membran air pump controlled with valves is connected to the viscometer. The flowtime of the liquid is measured by photoelectric beams. A high precision thermometer (PT 100) is attached for temperature measurement.

• The complete control of the measurement system is carried out with the help of the Windows program "ViscoMeasurement". The control program is connected to the pure component databank of the Dortmund Data Bank (DDB-PCP). We are able to run automatic temperature programs for high precision viscosity measurements up to 353 K (limited up to now by the thermostat) and a viscosity range from 0.3 to 100 mm²/s (cSt).

• A schematic drawing of the setup is shown in the following figure:

• Typical results of a measurement are plotted in the following diagram together with data from literature.

• The main window of the control program contains all important input and the current status of the measurement:

Concentric cylinder viscometer .

• The formulae derived apply to the measurement of Newtonian fluids, confined between concentric cylinders of infinite length, and neglecting any inertial effects [ref. 1]. The inner and outer cylinders are of radius R1 and R2 respectively, and rotate with a relative angular velocity O. Considering the fluid between the inner cylinder and a tadius r; each particle moves with a constant angular velocity, such that the net torque on the fluid is zero. The torque G per unit length on a cylindrical surface at radius r is

• G = 2 pi R1^2 s1 • where s1 is the shear stress on the inner cylinder, The shear stress

at any radius r is • s = G / 2 pi r^2 • and in particular, at the outer cylinder is • s2=G / 2 pi R2^2.

Figure 1: Horizontal section of a concentric cylinder

viscometer and deformation of a fluid element.

Viscometer Mechanism.

• Operation of the viscometer mechaalsm is now described, see figure 3; Complete engineering  drawings are shown in Appendix C. All major parts were machined from Dural, with the exception of the stirrer: the corrosive nature of the lubricants under study necessitates the use of glass for this component. In all experiments the assembly was suspended above the test fluid by a retort stand.

• A small DC motor (A) drives the disk (E), the outer edge of which is removed over 180 degrees, as shown in the detail. Disk (F) is also cut in a sirhilar way. Disks (E) and (F) may rotate independently about the same axis, due to the bearings in (E) and lower plate (C). The outer end of spiral hair spring (1) is bolted to (E), while the inner end slots into part (F). Therefore the lower disk (F) is indirectly driven by the upper disk (E), via torque spring (I). Connected to (F) by means of a pinned push-fit joint is the chuck (G). Three nylon screws in this component clamp the glass stirring rod (J) securely. The dimensions of the cylindrical, stirring end of (J) restrict the instrument to measurement over a certain range of viscosity. Different ranges can easily be obtained by altering the size of this stirring cylinder. In the following experiments two stirrers were used, one with a cylinder diameter of 2cm and length of 2cm, the other with a cylinder diameter of 1 cm and length 2cm.

• An infra-red light beam is emitted by the LED (L), and passes through the mechanism before detection by the photo diode (M). The LED cover (D) ensures that the beam is sufficiently narrow that reflections from parts of the mechanism do not disrupt readings.

• The mounting plates (B) and (C) are supported by four corner pillars, (K). Side plates (H) are fitted; these perform the multiple functions of increasing the rigidity of the structure, excluding dirt, and preventing ambient light from corrupting the infra-red beam measurements.

• In operation, the motor rotates at a speed up to 300 rpm, determined hy the control electronics (see section 3.2). The stirrer is turned via the spiral spring, which provides a torque proportional to its angular extension. Thus the relative angular displacement between disks (E) and (F) depends directly on the viscosity of the fluid and rotation rate (see section 2.3 theory). As described, parts (E) and (F) are cut away over 180 degrees; this causes the beam to be interrupted once per revolution. Calculation of the mark/space ratio results in the angular displacement, whilst the motor speed may be accurately determined from the period. Figure 4 illustrates the mechanism operation with liquids of different viscosities, and also shows the corresponding expected photo-diode outputs.

• A serious problem occurred with the spiral spring. Such a component is difficult to obtain commercially, consequently one was wound from a strip of plate brass approximately 30 cm long, 2 mm wide and 0.5 mm thick. Unfortunately the quality of the spring thus produced was unsatisfactory: only about 3 turns were possible and the spiral shape was difficult to muintain. In addition it was impossible to keep the spring planar: the result of this was that when mounted in the mechanism, the spring scraped on disks (E) and (F) (refer to figure 3). Undoubtedly the instrument's measurement accuracy was seriously affected by the additional friction, hysteresis and non-linearity of this component. Nevertheless useful results were obtalnable, as described in section 4, proving the principle and justifying future pursuit of a suitable spring.

• Figure 4: Operation of the viscometer mechanism. The diagrams on the left show the relative orientations of the rotating parts (E) and (F), those on the right show the type of photodiode outputs that may be expected

from these configurations.

Operating software .

• A ZX Spectrum computer running an assembler application was used as a development tool, to edit and compile the operating program prior to downloading into the microprocessor control system's EEPROM. A complete listing of the viscometer control software is presented in appendix B.

• A modular programming approach was adopted, and a library of subroutines for elementary functions developed (section 3.3.1). These are called from subroutines which perform statistical analysis, calculate the viscosity, control the period between measurements, and log data (section 3.3.2). These in turn are called from a main control program, under direct user control (section 3.3.3).

Function subroutines:

• The collection of subroutines perform the basic functions listed below [ref. 6 & 7]. A 5 byte floating point format is used, consisting of a 32-hit fractional part, 8-hit exponent part, and sign bit. The numbers so represented have a range of +/- 3.4 x 10^38, to a precision of one part in 4.3 x 10^9.

• 1-Clock/Timer: The 50Hz mains frequency counter is used to drive a real-time clock/timer, which may be displayed in either hours/minutes or hours/minutes/seconds format, according on the user's preference. The 50 Hz counter is 8-bit so in order to retain the correct time, the clock routine must be called at least every 5 seconds. In fact it is called more often, whenever the keyboard is scanned or readings taken, which in practice accounts for most of the processor's time.

• 2- Input routines: These scan the keyboard, accept user input of floating point decimal numbers, and convert to the normalised binary floating point format adopted.

• 3-Print routine: This allows the program to output a result to the display. The binary floating point number is converted to decimal, and leading zeros blanked.

• 4-Error handling: The user is informed of any measurement or arithmetical errors that have occurred. A list of the possible error codes that may be generated is shown in table I below.

• 5-Arithmetic functions: These operate on numbers in normalised floating point format, and perform the following operations: addition, subtraction, multiplication, reciprocal and division.

• 6-Read routines: These read the mark/space ratio and period of rotation, of the viscometer mechanism. If measurement of a viscosity outside the possible range is attempted, an appropriate error is indicated.

• 7-Reset: This routine monitors the 'RST' key; if it is pressed for longer thah 1/2 a second a system reset is pefformed. This is similar to switching the machine off and on again, except that none of the results or user defined parameters are erased, with the exception of the time and measurement interval.

• 8-Regld, Regsv: These two routines load/save the Z80's registers form/to the stack (upper part of the system memory that is used as temporary storage space by the processor). They are often called at the start and finish of a subroutine, in order that the Z80's registers are preserved by the routine.

Viscosity measurement subroutines: • The procedure for viscosity determination is shown in the flow

diagram, figure 6. First a useful measurement range is determined, by starting the motor at its maximum rate and gradually reducing the speed in steps until the displacement between the disks in the mechanism falls below 170 degrees. The lower end of the range is found by increasing the motor speed from zero until a displacement is first detected. In order that transitional oscillations in the spring or extreme damping have time to decay, five revolutions of the mechanism are allowed to pass at each speed before reading the angular displacement. Measurements near to the lower end of the range could suffer low resolution and hence inaccuracy; therefore a small amount is added here. Once these two limits have successfully been set, the processor proceeds to take ten readings of displacement angle at ten speeds equally spaced within the range. Again transitional effects are allowed to pass, by now walting for ten revolutions before reading, at each speed. A statistical analysis [ref. 8] performs a least squares best fit on the data, to find the gradient of the graph of displacement against speed (see section 2.3). This gradient is related to that obtained from a previous calibration reading, and the viscosity calculated.

• Having obtained the viscosity, it is then checked to ensure that it lies within a user specified range. If for instance if it becomes to large, no further measurements are taken. This useful function could also be used to sound an alarm if the viscosity of the test fluid deviated too greatly from a specified value. The viscosities are logged in the system memory, where there is space for up to six thousand results. After the experiment, these may be scanned by the operator.

3RD Relation Between Viscosity &

Temperature

Dependence of viscosity on temperature

• These experiments were intended to test the approximate viscosity-temperature relation mentioned in section 2.4.2. That is,

• v = A exp (Ev / k T(• where v is the kinematic viscosity, k Boltzmann's constant,

T the temperature, and A and Ev constants. The measurements were obtained using both the viscometer of this project (hereafter referred to as the project viscometer), and a Ferranti-Shirley cone-on-plate viscometer. Therefore a useful comparison between the two viscometers was also obtained.

• Two lubricants were tested: Dow Corning FS-1265 10000 cst lubricant, and Dow Coming DC200 1000 cst lubricant. These kinematic viscosities are stated by the manufacturer, however the temperature at which the viscosity is specified is not mentioned. However the aim of these experiments was not to determine absolute viscosities, rather to investigate the degree of temperature variation and correlation with an existing commercial viscometer. Hence both instruments were calibrated to read the stated viscosity at room temperature as a reference point.

• For the project viscometer measurements, 50 cm3 of the test fluid was contained in a small beaker of diameter 4 cm. This beaker was suspended in a temperature controlled oil bath. The temperature of the test fluid itself was additionally monitored using a digital thermometer, with a thermocouple immersed in the liquid.

• During the measurements ample time was allowed for the temperature to reach a stable value, usually slightly less than that of the oil bath due to heat losses from the test fluid. Temperature control is built in to the Ferranti-Shirley viscometer, which pumps heated oil through the instrument to heat the sample under investigation.

• Viscosity was measured at temperatures ranging from room temperature to about a hundred degrees centigrade. Above this temperature the oil bath becomes intolerably smelly. Numerical results are presented in Appendix 0.

• Figure 12 shows in graphical form the variation with temperature of the 10000 cst fluid. Calibration was performed at 22.5C. The data from the Ferrauti-Shirley instrument approximates the exponential curve extremely well, although that from the project viscometer displays a large spread. This was probably mainly due to the inadequacies of the spiral spring. Error bars plotted on the project viscometer measurements are for a 10% random variation. Temperature is measurable to an accuracy less than half a degree, and the Ferranti-Shirley instrument specifies a precision of under 3%. Thus in the interests of clarity error bars have not been plotted on these data points.

Figure 12: Viscosity/Temperature for the FS-1265

10000 cst fluid

• Figure 13 is a graph of viscosity against temperature for the 1000 cst fluid. Again the Ferranti-Shirley results appear more accurate than those of the project viscometer.

Figure 13: Viscosity / Temperature for the DC200 1000 cst fluid.

• These results show that the exponential viscosity-temperature relation is well approximated within the measurement range of the experiment. This is particularly apparent for the 10000 cst FS-1265 lubricant, which displays a rapid decay of viscosity with rising temperature.