Falling Ball Viscometer
Objective:
Purpose of the Falling Ball Viscometer experiment was to measure the viscosity of glycerin or glycerol by using falling ball viscometer technique.
Background:
When a body falls in a liquid under the force of gravity, it accelerates until weight of the body is balanced by the buoyancy force and drag force. Terminal velocity is gained by the body at this point. Viscosity of the liquid can be evaluated by measuring this terminal velocity of the body in the liquid.
In this experiment a steel sphere was allowed to fall in glycerol and dynamic viscosity of glycerol was measured by using above mentioned logic. Following diagram delineates a free body diagram of the steel sphere falling in a liquid -
After gaining terminal velocity by the sphere, a force balance yields
ΣF = 0 = W-FD -Fb ... (1)
where
W = weight of sphere (N), FD = drag force (N), Fb = buoyancy force (N).
The drag force is given by the expression
FD = C.ρl.(U^2).A/2 .(2)
where
C = drag coefficient (dimensionless), ρl = density ofliquid (kg/m3), U= terminal velocity of sphere (m/s),
A = (πD^2/4) = presented area of sphere (m2).
For Stokes flow or creeping flow (very slow flow) around a sphere, the drag coefficient is
C=24/Re ..(3)
where the Reynolds number, Re, is
Re = U.D. ρl /μl (4)
and
D = diameter of sphere (m)
ρl = density of liquid (kg/m3)
μl= dynamic viscosity of liquid (Pa . s)
Stokes flow is strictly valid only for Re < 1.
As per the principle of Archimedes, the buoyancy force of a submerged object is the weight of the liquid displaced by the object. So, the buoyancy force on the sphere is
Fb = γl . V (5)
where
γl = specific weight of liquid (N/m3)
V = volume of sphere (m ).
It is to be noted that W = γs V, where γs is the specific weight of the sphere. Combining Eqs (3) and (4) and substituting the result into Eq (2), then substituting Eqs (2) and (5) into Eq (1) and solving for μl, following expression can be derived
μl = (γs - γl).D^2/18.U ..(6)
Apparatus:
1000 ml graduated cylinder, 1 foot scale, stop watch, thermometer, glycerol, needle-nose pliers or tweezers, micrometer or vernier caliper, electronic scale, copper plated steel spheres (BB s), masking tape, ring stand
Procedure:
At first the diameter of 20 steel spheres were measured using the micrometer or vernier caliper. Then same steel spheres were weighed using the electronic scale. After this, graduated cylinder was filled with glycerol in such a way that no air bubble was entered in the cylinder. Then the cylinder was placed on a table and the base of the cylinder was secured to the table with duct tape. In the next step a piece of masking tape was placed on the cylinder about two inches below the surface of the glycerol and a second piece was placed 12 inches lower than the first piece. The thermometer was then immersed in the glycerol and it was secured to the ring stand so that the temperature of the glycerol could be measured during course of the experiment. A sphere was held about 1 inch beneath the surface of the glycerol in the centre of the cylinder by using the pliers and the sphere was released. The time, taken by the sphere to fall 12 inches as marked by the pieces of masking tape, was measured by using the stop watch. This procedure was repeated for all remaining 19 spheres and temperature was recorded. Finally the glycerol was poured back into the bottles and spheres were removed. The cylinder was cleaned and dried for future use.
Results:
In the following table experimental data were tabulated and values of U, Re, C, μl were calculated as per equations mentioned before. Density of glycerol considered 1.26 gm/cm3.
So, mean value of dynamic viscosity
= (1.115153 + 1.15086 + 1.065713 + 1.098673 + 1.1179 + 1.098673 + 1.13438 + 1.062966 + 1.082193 + 1.098673 + 1.106913 + 1.090433 + 1.071206 + 1.123393 + 1.115153 + 1.123393 + 1.030006 + 1.062966 + 1.054726 + 1.090433) /20
= 1.0946 Pa.s = 1.0946 x 10^ 3 centipoise
A theoretical value for the dynamic viscosity of glycerol as a function of temperature is given by
the equation :
log (μl x 10^2) = 32.1741 - 0.20448 T + (4.60137E-4) T^2 - (3.81826E-7) T^3 . (7)
putting T = 298.75 in above equation,
log (μl x 10^2) = 32.1741 - 61.0884 + 41.0673 – 10.18 = 1.9722
or, μl x 10^2 = 10 ^ (1.9722) = 93.8
or, μl = 0.938 Pa.s
So, theoretical value of dynamic viscosity of glycerol at 25.6 degree Celsius = 0.938 Pa.s.
Measured value of dynamic viscosity of glycerol at 25.6 degree Celsius = 1.0946 Pa.s
So, percentage difference = ((1.0946 -0.938)/0.938) x 100 = 16.695%.
Conclusion:
After the experiment and analyzing the result, it was found that the percentage difference between theoretical and measured value is considerably high. The possible source of error may be due to the confinement of the sphere by the walls of the cylinder, vibration during the time of the fall etc. However, knowledge about measuring viscosity of a liquid was gained by this Falling Ball Viscometer experiment and thus the object of this experiment was met .So, it can be concluded that the experiment was carried out successfully.
Answer of Questions:
- Measured dynamic viscosity of glycerol in units of centipoises is 1.0946 x 10^ 3 centipoise.
- The possible sources of error are due to the confinement of the sphere by the walls of the cylinder, vibration during the time of the fall etc.
- If the sphere collides with the side wall of the cylinder, terminal velocity can be affected.
- The accuracy can be improved by taking a cylinder of larger inner diameter.
- Yes, glycerol is a Newtonian fluid.
