Edexcel A Level (IAL) Physics-1.26 Core Practical 2: Investigating Viscosity- Study Notes- New Syllabus

CORE PRACTICAL 2: Determine the Viscosity of a Liquid Using the Falling-Ball Method

This practical uses Stokes’ Law to determine the viscosity of a liquid by measuring the terminal velocity of a small sphere (ball bearing) falling through it.

Aim

To determine the viscosity \( \eta \) of a liquid (e.g., glycerine) using Stokes’ Law:

\( F = 6\pi \eta r v \)

Apparatus

• Long transparent cylinder filled with test liquid (e.g., glycerine)
• Ball bearings of known radius \( r \)
• Meter ruler or marked scale on cylinder
• Stopwatch (or video timer for accuracy)
• Micrometer screw gauge (to measure radius)
• Tongs or tweezers
• Thermometer (viscosity depends on temperature)

Theory

When a sphere falls through a viscous liquid:

• Weight acts downward
• Upthrust acts upward
• Viscous drag acts upward

At terminal velocity, forces balance:

Weight − Upthrust = Drag

Using Stokes’ Law:

\( 6\pi \eta r v = \dfrac{4}{3}\pi r^3 g (\rho_s – \rho_f) \)

Rearranged to find viscosity:

\( \eta = \dfrac{2 r^2 g (\rho_s – \rho_f)}{9 v} \)

Procedure

1. Measure the radius \( r \) of the ball bearing using a micrometer.
2. Measure density of sphere \( \rho_s \) (or look up material density).
3. Measure density of fluid \( \rho_f \) (or use known value).
4. Fill the tube with liquid and mark two points vertically (e.g., 0.10 m apart).
5. Use tongs to release the ball gently so it does not touch the sides.
6. Allow the ball to accelerate and reach terminal velocity before it reaches the first mark.
7. Start the timer when the ball passes the upper mark.
8. Stop the timer when it passes the lower mark.
9. Repeat at least 5 times for reliability.
10. Repeat with different-sized spheres for improved accuracy.

Data Processing

1. Calculate terminal velocity:

\( v = \dfrac{\Delta s}{\Delta t} \)

2. Substitute \( r \), \( \rho_s \), \( \rho_f \), \( v \) into:

\( \eta = \dfrac{2 r^2 g (\rho_s – \rho_f)}{9 v} \)

3. Take an average viscosity from multiple trials.

Assumptions (Why Stokes’ Law Works Here)

• The sphere is small and smooth.
• The motion is slow (laminar flow).
• The fluid is Newtonian (constant viscosity).
• No turbulence occurs around the sphere.
• The falling ball is far from the tube walls (minimising wall effects).
• The temperature is constant (viscosity depends strongly on temperature).

Sources of Error

• Timing errors (ball passes quickly through marks).
• Difficulty identifying exact terminal velocity point.
• Ball touching tube walls increases drag.
• Temperature variation changes viscosity.
• Inaccurate measurement of radius \( r \).
• Density values may not be precise.

How to Improve Accuracy

• Use video tracking to measure time more accurately.
• Use a taller tube so the ball reaches terminal velocity more clearly.
• Perform the experiment in a temperature-controlled environment.
• Use multiple ball sizes and plot \( v \) vs. \( r^2 \).
• Ensure the sphere is released centrally and gently.
• Repeat measurements and average results.