To determine the coefficient of viscosity of glycerin by rotating cylinder method lab manual

Viscosity of Glycerin Experiment

1. Aim

To determine the coefficient of viscosity of glycerin using the rotating cylinder method.

2. Apparatus Used

Rotating cylinder viscometer setup
Glycerin sample
Two concentric cylinders (inner and outer)
Motor with variable speed control
Tachometer/rpm counter
Adjustable pulley system
Stop watch
Thermometer
Weighing balance
Vernier caliper
Micrometer screw gauge
Thread and weights/spring balance

3. Diagram

4. Theory

The rotating cylinder method for determining viscosity is based on the measurement of torque required to rotate a cylinder at a constant angular velocity when it is immersed in the fluid whose viscosity is to be determined.

When an inner cylinder rotates inside a stationary outer cylinder with the space between filled with glycerin, the viscous drag of the fluid creates a torque. The magnitude of this torque is directly proportional to the coefficient of viscosity of the fluid.

For two concentric cylinders with the inner one rotating and the outer one stationary, the torque ($\tau$) experienced by the rotating cylinder due to viscous drag is given by:

$$\tau = \frac{4\pi\eta L \omega R_1^2 R_2^2}{R_2^2 - R_1^2}$$

Where:

$\eta$ (eta) = coefficient of viscosity
$L$ = height of the rotating cylinder in contact with the fluid
$\omega$ (omega) = angular velocity of the rotating cylinder
$R_1$ = radius of the inner cylinder
$R_2$ = radius of the outer cylinder

This relationship is derived from the fundamental principles of fluid mechanics. The viscous fluid between the cylinders is subjected to shear stress which is proportional to the rate of shear strain and the coefficient of viscosity. The torque required to maintain rotation is directly proportional to the viscosity of the fluid.

5. Formula

From the measured torque and angular velocity, we can determine the coefficient of viscosity using:

$$\eta = \frac{\tau(R_2^2 - R_1^2)}{4\pi L \omega R_1^2 R_2^2}$$

In practical terms, the torque can be measured by:

Using the applied force ($F$) and the effective radius of the pulley ($r$): $\tau = F \times r$
Or by measuring the tension in the thread connected to a weight: $\tau = (M - m)g \times r$

Where:

$M$ = mass applied to produce rotation
$m$ = mass required to overcome the friction of bearings (determined separately)
$g$ = acceleration due to gravity
$r$ = radius of the pulley

Finally, the coefficient of viscosity is:

$$\eta = \frac{(M - m)g \times r(R_2^2 - R_1^2)}{4\pi L \omega R_1^2 R_2^2}$$

Where $\omega = 2\pi N/60$ and $N$ is the speed in rpm.

6. Procedure

Setup Preparation:

Measure the dimensions of the inner and outer cylinders (radii $R_1$ and $R_2$) using the vernier caliper.
Measure the effective height ($L$) of the inner cylinder that will be immersed in glycerin.
Set up the rotating cylinder apparatus, ensuring the cylinders are concentric.
Clean the cylinders thoroughly and dry them.

System Calibration:

Determine the frictional torque of the system by running the inner cylinder without glycerin.
Record the minimum weight ($m$) required to overcome friction and initiate rotation.

Experiment Execution:

Fill the space between the cylinders with glycerin up to the marked height.
Record the temperature of glycerin using the thermometer.
Attach a known weight ($M$) to the thread wound around the pulley.
Release the weight and measure the steady rotational speed ($N$) using the tachometer.
Repeat steps for at least 5 different weights to obtain multiple data points.
For each weight, take 3 readings and use the average value for calculations.

Additional Measurements:

Measure the radius of the pulley ($r$) using the micrometer.
Record the room temperature.

7. Observation Table

Table 1: Dimensions of the Apparatus

Parameter	Symbol	Measured Value	Unit
Radius of inner cylinder	$R_1$	...	m
Radius of outer cylinder	$R_2$	...	m
Effective height of cylinder	$L$	...	m
Radius of pulley	$r$	...	m
Frictional mass	$m$	...	kg

Table 2: Experimental Observations

S.No.	Applied Mass ($M$)	Angular Speed ($N$)	Temperature of Glycerin
	(kg)	(rpm)	(°C)
1
2
3
4
5

8. Calculations

For each observation:

Calculate the effective torque: $\tau = (M - m)g \times r$
Convert rotational speed to angular velocity: $\omega = 2\pi N/60$
Calculate viscosity using the formula:
$$\eta = \frac{(M - m)g \times r(R_2^2 - R_1^2)}{4\pi L \omega R_1^2 R_2^2}$$
Calculate the mean value of $\eta$ from all observations.
Calculate the standard deviation to determine the precision of the measurements.

Sample Calculation (for the first observation):

Torque ($\tau$) = $(M_1 - m)g \times r = $ ... N·m
Angular velocity ($\omega$) = $2\pi \times N_1/60 = $ ... rad/s
Coefficient of viscosity ($\eta$) = ... Pa·s

9. Result

The coefficient of viscosity of glycerin at temperature T = ... °C is found to be $\eta = $ ... $\pm$ ... Pa·s (or Poise).

10. Precautions

Ensure the inner and outer cylinders are perfectly concentric to avoid uneven fluid distribution.
The inner cylinder should not touch the outer cylinder during rotation.
Take measurements only after the system has reached a steady rotational speed.
Keep the temperature constant throughout the experiment as viscosity is strongly temperature-dependent.
Clean all surfaces thoroughly before filling with glycerin to avoid contamination.
Avoid air bubbles in the glycerin sample.
Ensure that the thread does not slip on the pulley.
Maintain a slow and controlled release of weights to achieve steady rotation.
Take multiple readings and use the average for better accuracy.
Allow sufficient time for the glycerin to reach equilibrium temperature.

11. Viva Voce Questions

Q1: What is viscosity and what is its SI unit?

Viscosity is the measure of a fluid's resistance to flow. It's the property of a fluid that causes it to resist relative motion of its molecules. The SI unit of viscosity is Pascal-second (Pa·s) or N·s/m².

Q2: How does temperature affect the viscosity of glycerin?

The viscosity of glycerin decreases with increasing temperature. This is because higher temperatures increase the kinetic energy of molecules, reducing intermolecular forces and allowing them to flow more easily past each other.

Q3: Why do we use concentric cylinders in this experiment?

Concentric cylinders provide a uniform gap for the fluid, ensuring laminar flow and uniform distribution of shear stress throughout the fluid, which allows for accurate measurement of viscosity.

Q4: What are Newtonian and non-Newtonian fluids? Is glycerin a Newtonian fluid?

Newtonian fluids maintain a constant viscosity regardless of the applied stress or strain rate. Non-Newtonian fluids have viscosities that change with applied stress or strain rate. Glycerin is typically a Newtonian fluid under normal conditions.

Q5: Why is it necessary to determine the frictional torque separately?

The frictional torque from bearings and other mechanical parts of the apparatus creates additional resistance not related to the fluid's viscosity. Subtracting this value gives us the true torque due to fluid viscosity alone.

Q6: What other methods can be used to determine viscosity?

Other methods include the falling sphere method, capillary tube method, Ostwald viscometer, Saybolt viscometer, and Brookfield viscometer.

Q7: How would the results differ if we used water instead of glycerin?

Water has a much lower viscosity than glycerin (about 1000 times less at room temperature). This would require either a more sensitive measuring apparatus or much higher rotation speeds to obtain measurable torque values.

Q8: What sources of error might affect the accuracy of this experiment?

Possible errors include temperature fluctuations, non-concentricity of cylinders, slippage of thread on pulley, air bubbles in the sample, end effects of the cylinder, and instrument calibration errors.

Q9: Why is the rotating cylinder method preferred over other methods for highly viscous fluids?

The rotating cylinder method works well for highly viscous fluids because it creates a well-defined shear rate, operates continuously, and can handle a wide range of viscosities without clogging or other issues that might affect capillary methods.

Q10: How does the gap width between cylinders affect the measurement?

A smaller gap provides more accurate results for Newtonian fluids but requires more precise alignment. For very viscous fluids, a larger gap may be needed to avoid excessive torque requirements. The gap width is incorporated in the formula as $(R_2^2 - R_1^2)$.