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 Procedure: 1. Drop a medium sized ball into the column of glycerine and make a starting mark close to the top of the column, but at a position at which the ball has achieved terminal velocity (ie constant velocity), and a finishing mark close to the bottom. The distance between the marks is the fixed distance s. Now it is required to time balls of varying r when falling through that distance s between the two marks. Measure the diameter D of each ball with a micrometer before dropping it into the glycerine and measuring t. Take about 8 readings of t for a wide range of r. 3. Plot a graph of r2 versus uncertainties). 4. To determine the density of the steel balls, and because all balls were manufactured from the same melt, it is necessary only to measure mass and volume of one large steel ball ( = m/V). The density of glycerine L can be determined using a hydrometer. Use equation (9) to calculate .

2.

1 and determine a value for the slope k (without t

5. 6.

Compare the calculated value of with the tabulated data. Note the temperature dependence and record the temperature at which this experiment was performed. Note also that the viscosity of glycerine is very dependent on water content.

3

EXAMPLE LAB REPORT - VISCOSITY OF GLYCERINE Introduction – See lab report Method – See lab report Results When the steel balls were dropped into the cylinder they appeared to reach their terminal velocity within the first 30 cm. The time was, therefore, recorded between a line marked on the cylinder 30 cm below the surface and a second line 50 cm below the first. The measured diameters, d, of the steel balls and the time taken for them to fall through 0.5 m of glycerine are shown in table 1. The calculated value of (1/r)2 is also shown. The diameter was measured with a set of callipers and the error in the reading was ± 0.05 mm. The time was measured with a digital stop watch with an error of ±0.05 s. r-2(m-2)

d (mm)

t(s)

d(m)

r(m)

1.1 72.8 0.0011...