Lecture Notes: Calculating Viscosity Using a Spherical Object

Introduction

• Speaker: Farah Malone
• Topic: Calculating the viscosity of a fluid using a spherical object.
• Method involves a simple experiment.

Materials Required

• Stopwatch
• Magnet bar
• Graduated cylinder
• Fluid (unknown viscosity)
• Steel ball (or any spherical ball of known density)

Experimental Setup

1. Mark Graduated Cylinder: Indicate lengths between ticks on the cylinder.
2. Fill Graduated Cylinder: Use fluid of unknown viscosity.
3. Drop Spherical Ball: Use a steel ball or any ball with known density.
4. Removal: Use a magnet bar to remove the steel ball.
5. Repetition: Conduct multiple trials for accuracy.

Forces at Terminal Velocity

• Positive Y-Direction: Drag force + Buoyant force.
• Negative Y-Direction: Gravitational force.

Understanding Drag Force

• Derived through Stokes Law:
  • Drag force depends on size of sphere, terminal velocity, coefficient of viscosity.
  • Equation: Drag Force = K * R^a * Viscosity^b * Velocity^c
  • Unit derivation: a = 1, b = 1, c = 1
  • K is a constant: K = 6π
  • Final Equation: Drag Force = 6π * Viscosity * Radius * Terminal Velocity

Terminal Velocity

• Defined as the speed where the ball stops accelerating in the fluid.

Calculating Viscosity

• Equilibrium at Terminal Velocity:
  • Sum of forces = 0
  • Drag Force + Buoyant Force - Gravitational Force = 0
• Equation Derivation:
  • Drag Force = 6π * Viscosity * Radius * Terminal Velocity
  • mg - Buoyant Force = (4/3)πR^3 * (Density of Ball - Density of Fluid) * Gravity
• Final Viscosity Formula:
  • Viscosity = (2/9) * R^2 * (Density of Ball - Density of Fluid) * Gravity / Terminal Velocity
• Simplified Formula for Experiment:
  • Viscosity = D^2 * (Density of Ball - Density of Fluid) * Gravity * Time / (18 * Length)
  • Time: Duration of ball traveling through the length.

Conclusion

• The method provides a simple way to calculate viscosity.
• Useful in laboratories or classrooms.
• Encouraged to read references for further understanding.

References

• Not specifically mentioned but encouraged to explore for more information.