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.
However not in sucrose, the RBCs were semi-permeable. RBCs diffuse in the water around five minutes, but in glycerol RBCs diffuse in fifteen minutes. Several factors are involved that affect the rate at which the RBCs diffuse, could have been because of the size, polarity, or the charge of the molecule. Urea is the carbonic acid found in urine, blood, and lymph; it is formed in the liver from amino acids and ammonia. It is important that urea is permeable because the amount of urea in the body is essential because it helps undergo waste product. Glycerol is combination of sugar and alcohol. This solution is an important component for storage of fats that are ingested into the body as food, this one good reason why glycerol is permeable. Sucrose however has low permeability which is why sucrose has a slow rate of diffusion and glycerol and urea on the other hand has fast rates of
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