Viscosity of Glycerine
1
LAB SHEET - VISCOSITY OF GLYCERINE Aim: To measure the viscosity of glycerine using Stokes ' method in which steel balls are allowed to fall through glycerine. Theory: (i) If a body of mass m falls through a viscous fluid, it will accelerate until the combination of the viscous force (or drag) FD, and the buoyancy force FB balance the gravitational force Fg (= mg) FD + FB = Fg (1)
When this equilibrium is reached, the body continues to fall, but at a constant velocity, called the terminal velocity. (ii) Archimedes ' Principle states that the buoyancy force acting on a body immersed in a fluid is equal to the weight of the fluid displaced. If the body immersed is a sphere of volume V and radius r, the volume of fluid displaced is also V. Thus if the density of the fluid is L, FB = VLg 4 = r3 Lg 3 (iii)
(2)
Stokes showed that for a sphere of radius r moving through a fluid of viscosity , the viscous drag is FD = 6vr (3) where v is the steady velocity.
(iv)
If the density of the sphere is S, then the gravitational force is 4 Fg = 3 r3 Sg (4)
(v)
Substituting (2), (3) and (4) into (1) 4 4 6vr + 3 r3 Lg = 3 r3Sg 4 3 r (S – L)g = 6vr 3 r2 =
9 2 (S L ) g
v
(5)
The terminal velocity v can be determined by measuring the time t for steel balls to fall through a fixed distance s s v= (6) t Substituting this expression into (5) gives
r2
9 s 2 (S L ) g t
2
So
r2 k
1 t
(7)
where
k
s 9 2 (S L ) g
(8)
Now we can see that, if the time t for steel balls of varying radius r to fall at terminal velocity through the fixed distance s can be measured, a plot of r2 against 1/t should yield a straight line of slope k. Rearranging (8)
2k ( S L ) g 9s
(9)
To be able to calculate the viscosity of glycerine, , experimental data are required for the gradient k, the fixed distance s, the density of the sphere S and the density of the liquid L
LAB SHEET - VISCOSITY OF GLYCERINE Aim: To measure the viscosity of glycerine using Stokes ' method in which steel balls are allowed to fall through glycerine. Theory: (i) If a body of mass m falls through a viscous fluid, it will accelerate until the combination of the viscous force (or drag) FD, and the buoyancy force FB balance the gravitational force Fg (= mg) FD + FB = Fg (1)
When this equilibrium is reached, the body continues to fall, but at a constant velocity, called the terminal velocity. (ii) Archimedes ' Principle states that the buoyancy force acting on a body immersed in a fluid is equal to the weight of the fluid displaced. If the body immersed is a sphere of volume V and radius r, the volume of fluid displaced is also V. Thus if the density of the fluid is L, FB = VLg 4 = r3 Lg 3 (iii)
(2)
Stokes showed that for a sphere of radius r moving through a fluid of viscosity , the viscous drag is FD = 6vr (3) where v is the steady velocity.
(iv)
If the density of the sphere is S, then the gravitational force is 4 Fg = 3 r3 Sg (4)
(v)
Substituting (2), (3) and (4) into (1) 4 4 6vr + 3 r3 Lg = 3 r3Sg 4 3 r (S – L)g = 6vr 3 r2 =
9 2 (S L ) g
v
(5)
The terminal velocity v can be determined by measuring the time t for steel balls to fall through a fixed distance s s v= (6) t Substituting this expression into (5) gives
r2
9 s 2 (S L ) g t
2
So
r2 k
1 t
(7)
where
k
s 9 2 (S L ) g
(8)
Now we can see that, if the time t for steel balls of varying radius r to fall at terminal velocity through the fixed distance s can be measured, a plot of r2 against 1/t should yield a straight line of slope k. Rearranging (8)
2k ( S L ) g 9s
(9)
To be able to calculate the viscosity of glycerine, , experimental data are required for the gradient k, the fixed distance s, the density of the sphere S and the density of the liquid L
Bibliography: [1] Brown, J. Y. and Heath W. L. Table of Physical Constants. Paragon Press, London 1985. [2] http://www.binacchi.com/Utilites/useful/glycerine%20viscosity.pdf. Accessed 22/07/2010. 5