Experiment

KWAME NKRUMAH UNIVERSITYOF SCIENCE AND TECHNOLOGY COLLEGE OF SCIENCE DEPARTMENT OF PHYSICS AN EXPERIMENT PERFORMED TO DETERMINE THE RATE OF VISCOSITY OF WATER, METHANOL AND DIFFERENT COMPOSITIONS OF WATER–METHANOL MIXTURES, USING THE FALLING BALL VISCOMETER DATE: 15/10/2013 GROUP 1 KWAKYE SAMUEL KWABENA 8060912 ANDZIE – BOATENG STELLA 5043910 ABSTRACT The viscosity of a fluid is an important property in the analysis of liquid behavior and fluid motion near solid boundaries. The viscosity is the fluid resistance to shear or flow and is a measure of the adhesive and cohesive or frictional fluid property. The resistance is caused by intermolecular friction exerted when layers of fluid attempt to slide by one another. Viscosity is a measure of a fluids resistance to flow. A Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity. For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure and also on the chemical composition of the fluid if the fluid is not a pure substance not on the forces acting upon it. Due to internal friction among their particles, liquids and gases have different viscosities. The viscosity, a function of the substance’s structure and its temperature can be experimentally determined, for example, by measuring the rate of fall of a ball in a tube filled with the liquid to be investigated. EXPERIMENTAL SET-UP: VISCOSITY MEASUREMENTS WITH THE FALLING BALL VISCOMETER THEORY AND EVALUATION The dynamic viscosity ὴ of a liquid is defined by the force F which is required to move two parallel layers of liquid both having the area A and separated by dx with the velocity dw with respect to each other ὴ=FAdwdx By relating the dynamic viscosity to the density p of the liquid, one obtains the kinematic viscosity v; the reciprocal of the dynamic viscosity is designated as fluidity ⱷ v=ὴp ⱷ=1ὴ A spherical particle with a radius r moves in a liquid under the influence of a force F and the viscosity ⱷ with a constant velocity ῳ ῳ=F6πὴr For the fall of a sphere in the gravitational field of the earth the motive force F is equal to the product of the acceleration of gravity g and the effective mass m, which can be expressed as the density difference between the sphere (p1) and the liquid (p2) F=mg=43πr3g(p1-p2) The correlation for the calculation of the viscosity, which is a derived from (4) and (5) is only considered as the limit law for expanded media (the radius can be neglected with respect to that of the gravity tube); otherwise, the relationship can be approximated by corrections (Ladenburg Correction). ὴ=2gp1-p2r2gw for commercial falling ball viscometers with sets of calibrated spheres, the constants in equation (6) are combined with the operative factors to form the spherical constant K; this makes the calculations much easier. ὴ= K t (p1-p2) (t = rate of fall of the sphere for a measuring distance of s= 100mm) The density p2 of the liquid at temperature T which is contained in equation (7) can be calculated using the relationship p2=mV (m= mass of the liquid; V= volume of the pycnometer) Using the experimentally determined pycnometer data or alternatively that obtained from tables 1 and 2. The viscosity is a function of the structure of the system and temperature. The alteration in the measured viscosity in which the composition of methanol-water are expressed as the mass fraction w (9.1) or the mole fraction x (9.2) is an expression of the non-ideal behavior of the liquids. It correlates to additional mixing phenomena such as mixing volume (volume contraction) and mixing enthalpy. w1=m1m1+m2 (w1= mass fraction, m1=mass of substance 1) E x1=n1n1+n2=m1M1m1M1+m2M2 (x1= mole fraction, n1=quantity of substance, m1=mass of the substance 1, M1= molar mass of substance 1) For many liquids the reduction of the viscosity with temperature is described by an empirically determined exponential function (10) 1ὴ=ⱷ=Ce-E/RT (R=8.31441 J.K-1.mol-1 universal gas constant) In this relationship which is analogous to the Arrhenius equation. C represents a system-dependent constant; E is an expression of the molar energy which is required to overcome the internal friction. This activation energy can be determined from the slope obtained by the linear relation (10.1) between In ὴ and 1/T (fig. 4) In ὴ =E/R -1/T –In C TABLE OF OBSERVATIONS TABLE 1.1 (WATER) T/K | P/gcm-3 | ὴmPa.s | 303.15 | 0.8083 | 0.09 | 308.15 | 0.8081 | 0.08 | 313.15 | 0.8078 | 0.09 | 318.15 | 0.8056 | 0.10 | 323.15 | 0.8038 | 0.12 | TABLE 1.2 (METHANOL) T/K | P/gcm-3 | ὴmPa.s | 303.15 | 0.6483 | 0.16 | 308.15 | 0.6471 | 0.17 | 313.15 | 0.6457 | 0.17 | 318.15 | 0.6441 | 0.18 | 323.15 | 0.6421 | 0.17 | TABLE 1.3 (METHANOL-WATER MIXTURES) m (CH3OH)/g | m (H2O)/g | P/gcm-3 | ὴmPa.s | 0 | 100 | 0.7233 | 0.13 | 10 | 90 | 0.7221 | 0.13 | 20 | 80 | 0.7207 | 0.13 | 30 | 70 | 0.7200 | 0.14 | 40 | 60 | 0.7190 | 0.13 | 50 | 50 | 0.7180 | 0.18 | GRAPHS OF RESULTS GRAPH 1.1 GRAPH 1.2 GRAPH 1.3 CALCULATIONS The measurements are time consuming and take approximately ten hours when performed. The investigations conducted on the temperature dependence of the viscosity of pure liquids in steps of 5 K in the temperature range between 303.15 and 323.15. The density of water, methanol, and methanol water mixtures was determined at each temperature range, with first weighing the pycnometer and filling it with the desired liquid, weighed again and difference in mass noted accordingly for the various temperature ranges. Mathematically density (p)= m/v, But v= 30ml = 30cm3 The dynamic viscosity ὴ is calculated from ὴ=FAdw/dx the time taken for the borosilicate glass to fall in the viscometer for each temperature range is done five times and then the average calculated for. This is done for all other mediums volume (v)=30 ml =30 cm3 mass of pycnometer = 24.24 g mass of pycnometer and methanol = 43.70 g mass of pycnometer, methanol, and water =45.92 g mass of pycnometer and water = 48.49 g Unit for density is g/cm3 That of viscosity is mPa.s DATA AND RESULTS The experimentally determined viscosities are presented graphically in the graph 1.1, 1.2, and 1.3 as a function of the composition of water, methanol, and water-methanol compositions. The slopes of the line can be calculated from the following relationships between In ὴ and 1/T and also from linear regression analysis. DISCUSSION AND CONCLUSION The viscosity of a fluid is an important property in the analysis of liquid behavior and fluid motion near solid boundaries. The viscosity is the fluid resistance to shear or flow and is a measure of the adhesive and cohesive or frictional fluid property. This experiment covers the viscosity measurements in different mixtures. From experimental values the dynamic and kinematic viscosities. From the experiment it can be deducted also that the rate of cohesive and adhesive interactions decrease as temperature rises.