EXPERIMENT: To determine the coefficient of viscosity of glycerin by Stoke's method
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1. AIM
To determine the coefficient of viscosity of glycerin by observing the terminal velocity of a spherical body falling through it.
2. APPARATUS USED
- A long glass cylindrical tube/jar (about 100 cm in height and 5 cm in diameter)
- Glycerin of sufficient quantity to fill the tube
- Small steel/glass spherical balls of different diameters
- Micrometer screw gauge
- Vernier calipers
- Stopwatch with least count 0.1 s
- Meter scale
- Thermometer
- Graph paper
- Thread and forceps
- Cleaning cloth and tissue paper
- Stand with clamp (to hold the cylindrical tube)
- Weighing balance
3. DIAGRAM
4. THEORY
When a spherical body falls through a viscous fluid, it experiences three forces:
-
Weight of the sphere (W): Acts vertically downward
\[ W = \frac{4}{3}\pi r^3 \rho_s g \]
-
Upthrust or Buoyant force (U): Acts vertically upward
\[ U = \frac{4}{3}\pi r^3 \rho g \]
-
Viscous force (F): Acts vertically upward (opposite to motion)
\[ F = 6\pi\eta rv \text{ (Stoke's Law)} \]
Where:
- \( r \) = radius of the sphere
- \( \rho_s \) = density of the sphere material
- \( \rho \) = density of the fluid (glycerin)
- \( g \) = acceleration due to gravity
- \( \eta \) = coefficient of viscosity of the fluid
- \( v \) = velocity of the sphere
Initially, when the sphere is dropped into the fluid, its velocity increases. However, as the velocity increases, the viscous force also increases. Eventually, the sphere reaches a constant velocity called terminal velocity (\(v_1\)) when all forces balance each other:
\[ \text{Weight} = \text{Upthrust} + \text{Viscous force} \]
\[ \frac{4}{3}\pi r^3 \rho_s g = \frac{4}{3}\pi r^3 \rho g + 6\pi\eta r v_1 \]
Rearranging:
\[ \frac{4}{3}\pi r^3 g(\rho_s - \rho) = 6\pi\eta r v_1 \]
Solving for \(\eta\):
\[ \eta = \frac{2r^2 g(\rho_s - \rho)}{9v_1} \]
This is the formula used to calculate the coefficient of viscosity by Stoke's method.
5. FORMULA
The coefficient of viscosity of the fluid (glycerin) is given by:
\[ \eta = \frac{2r^2 g(\rho_s - \rho)}{9v_1} \]
Where:
- \( \eta \) = coefficient of viscosity of glycerin (in poise or N·s/m²)
- \( r \) = radius of the spherical ball (in m)
- \( g \) = acceleration due to gravity (9.8 m/s²)
- \( \rho_s \) = density of the material of the ball (in kg/m³)
- \( \rho \) = density of glycerin (in kg/m³)
- \( v_1 \) = terminal velocity of the ball in glycerin (in m/s)
The terminal velocity \(v_1\) is calculated as:
\[ v_1 = \frac{h}{t} \]
Where:
- \( h \) = distance between two reference marks (in m)
- \( t \) = time taken by the ball to travel distance h (in s)
6. PROCEDURE
- Clean the glass tube thoroughly and mount it vertically using the stand and clamp.
- Fill the tube with glycerin up to about 80% of its height.
- Mark two reference points A and B on the tube, maintaining a sufficient distance between them (usually 50-60 cm). Ensure that point A is sufficiently below the glycerin surface to allow the ball to attain terminal velocity before reaching it.
- Measure the diameter of several steel balls using a micrometer screw gauge and calculate their radii.
- Measure the temperature of glycerin using the thermometer and note it down.
- Gently drop a steel ball at the center of the tube and start the stopwatch as the ball passes mark A.
- Stop the stopwatch when the ball passes mark B and record the time.
- Repeat steps 6-7 for the same ball at least three times to get an average reading.
- Repeat steps 4-8 with balls of different diameters.
- Measure the distance between marks A and B accurately.
- Note down the density of the steel ball and the density of glycerin at the experimental temperature from standard tables or determine them experimentally.
- Calculate the coefficient of viscosity using the formula.
7. OBSERVATION TABLE
Table 1: Measurement of diameter of the spherical balls
| Ball No. | Micrometer Screw Gauge Readings | Mean Diameter (d) mm | Radius (r) mm | |||
|---|---|---|---|---|---|---|
| M.S.R. (mm) | Zero Error (mm) | C.S.R. × L.C. (mm) | Corrected Reading (mm) | |||
| 1 | ||||||
| 2 | ||||||
| 3 | ||||||
| 4 | ||||||
| 5 | ||||||
Table 2: Measurement of time of fall
| Ball No. | Radius (r) m | Distance between marks (h) m | Time of fall (s) | Mean time (t) s | Terminal velocity v₁ = h/t (m/s) | ||
|---|---|---|---|---|---|---|---|
| t₁ | t₂ | t₃ | |||||
| 1 | |||||||
| 2 | |||||||
| 3 | |||||||
| 4 | |||||||
| 5 | |||||||
Table 3: Calculation of coefficient of viscosity
| Ball No. | Radius (r) m | Terminal velocity (v₁) m/s | Coefficient of viscosity (η) N·s/m² |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 |
Mean value of coefficient of viscosity, η = ________ N·s/m² or ________ poise
8. CALCULATIONS
For each ball:
- Calculate the radius (r) from the measured diameter.
- Calculate the terminal velocity using \(v_1 = \frac{h}{t}\), where h is the distance between marks A and B, and t is the time taken.
- Calculate the coefficient of viscosity using:
\[ \eta = \frac{2r^2 g(\rho_s - \rho)}{9v_1} \]
Given:
- g = 9.8 m/s²
- \(\rho_s\) = ________ kg/m³ (density of steel ball)
- \(\rho\) = ________ kg/m³ (density of glycerin at experimental temperature)
4. Calculate the mean value of η from all observations.
Sample calculation for Ball No. 1:
Given:
Radius of ball (r) = ________ m
Distance between marks (h) = ________ m
Mean time of fall (t) = ________ s
Terminal velocity (v₁) = h/t = ________ / ________ = ________ m/s
Coefficient of viscosity (η) = [2r²g(ρₛ - ρ)]/9v₁
= [2 × (______)² × 9.8 × (______ - ______)]/[9 × ______]
= ________ N·s/m²
Radius of ball (r) = ________ m
Distance between marks (h) = ________ m
Mean time of fall (t) = ________ s
Terminal velocity (v₁) = h/t = ________ / ________ = ________ m/s
Coefficient of viscosity (η) = [2r²g(ρₛ - ρ)]/9v₁
= [2 × (______)² × 9.8 × (______ - ______)]/[9 × ______]
= ________ N·s/m²
9. RESULT
The coefficient of viscosity of glycerin at ________ °C is found to be:
\[ \eta = \text{________} \text{ N·s/m²} \text{ or } \text{________} \text{ poise} \]
10. PRECAUTIONS
- The cylindrical tube should be kept perfectly vertical.
- The balls should be clean, smooth, and perfectly spherical.
- The diameter of the balls should be measured accurately using a micrometer screw gauge.
- The balls should be dropped exactly at the center of the tube to avoid wall effects.
- The reference marks A and B should be clearly visible.
- Mark A should be sufficiently below the glycerin surface to ensure the ball reaches terminal velocity before passing it.
- The spherical balls should be small compared to the diameter of the tube (diameter of ball < 1/10 of tube diameter) to minimize wall effects.
- The temperature of glycerin should be noted as viscosity is highly temperature-dependent.
- Avoid air bubbles in glycerin as they affect the falling velocity.
- The stopwatch should be started and stopped exactly when the ball passes the reference marks.
- Each measurement should be repeated several times to minimize random errors.
- The density values used should correspond to the experimental temperature.
11. VIVA VOICE QUESTIONS
Q: What is viscosity and what causes it?
A: Viscosity is the measure of a fluid's resistance to flow. It is caused by the internal friction between the molecules of the fluid. In liquids, it is primarily due to intermolecular cohesive forces.
Q: State Stoke's law and its limitations.
A: Stoke's law states that the viscous drag force on a spherical object moving through a viscous fluid is given by F = 6πηrv, where η is the coefficient of viscosity, r is the radius of the sphere, and v is its velocity. Limitations include: (i) it is valid only for laminar flow (Reynolds number < 0.5), (ii) the fluid must be homogeneous and extend infinitely in all directions, (iii) the sphere must be rigid and smooth, and (iv) there should be no wall effects.
Q: How does the viscosity of glycerin vary with temperature?
A: The viscosity of glycerin decreases significantly with increasing temperature. This is because higher temperatures provide more thermal energy to the molecules, reducing the intermolecular forces and allowing them to move past each other more easily.
Q: Why do we allow the sphere to fall some distance before starting measurements?
A: The sphere needs some distance to accelerate and reach its terminal velocity. We start our measurements only after the sphere has attained terminal velocity to ensure accurate results.
Q: How would the results be affected if the tube diameter was too small compared to the ball diameter?
A: If the tube diameter is too small compared to the ball diameter (typically less than 10 times), the proximity of the walls increases the drag force on the ball. This is called the "wall effect" and it results in a lower terminal velocity and consequently a higher calculated viscosity than the actual value.
Q: Why is it important to ensure that the steel ball falls through the center of the tube?
A: To minimize wall effects and ensure that the ball experiences uniform viscous resistance from all sides. If the ball falls near the wall, it experiences additional drag due to boundary layer effects.
Q: What is terminal velocity and how is it reached?
A: Terminal velocity is the constant velocity attained by a falling object when the drag force equals the gravitational force. Initially, when the ball is released, it accelerates due to gravity. As the velocity increases, the viscous resistance also increases. When the sum of viscous force and buoyant force exactly equals the weight of the ball, there is no net force and the ball moves with constant velocity (terminal velocity).
Q: Why does a steel ball fall faster in water than in glycerin?
A: Glycerin has a much higher viscosity than water. According to Stoke's law, the viscous drag force is directly proportional to the viscosity of the fluid. Therefore, the higher viscosity of glycerin results in a greater drag force, leading to a lower terminal velocity.
Q: How would the results change if you used a more dense ball of the same size?
A: A denser ball has a greater weight for the same volume. This leads to a higher terminal velocity and consequently a more accurate measurement of viscosity, especially for highly viscous fluids like glycerin.
Q: What are the sources of error in this experiment?
A: Sources of error include: (i) inaccurate measurement of ball diameter, (ii) non-spherical balls, (iii) temperature variations affecting viscosity, (iv) wall effects if the tube is too narrow, (v) errors in timing, (vi) non-attainment of terminal velocity before measurement starts, (vii) air bubbles in glycerin, and (viii) inaccurate values of densities.