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 ...
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...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:
1. Measured dynamic viscosity of glycerol in units of centipoises is 1.0946 x 10^ 3 centipoise.
2. 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.
3. If the sphere collides with the side wall of the cylinder, terminal velocity can be affected.
4. The accuracy can be improved by taking a cylinder of larger inner diameter.
5. Yes, glycerol is a Newtonian fluid.
They just forgot to mention the other effects of fluids in nature. “The influence of the fluid on a body moving through it depends not only on the body’s velocity but also on the velocity of the fluid,” this is called relative velocity ( ). The relative velocity of a body in a fluid has an effect on the magnitude of the acting forces. For example, as a long distance runner is running into a head wind, the force of the fluid is very strong. If the runner is running with the help of a tail wind, the current’s force is reduced and may even be unnoticeable.
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tube drops freely because there is nothing to hold it up or to resist its fall.
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states that "a body immersed in a fluid is buoyed up by a force equal the weight
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