F144 - Kecepatan terminal fluida statis ,hukum Stokes dalam fluida

Introduction

This tutorial covers the concept of terminal velocity in static fluids and Stokes' Law, as discussed in the video. Understanding these principles is essential for students in basic physics and for anyone interested in fluid mechanics. We will break down the derivation of the terminal velocity formula and provide examples to clarify the concepts.

Step 1: Understand Terminal Velocity

• Definition: Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium prevents further acceleration.
• Factors Influencing Terminal Velocity:
  • Size and shape of the object
  • Density of the fluid
  • Viscosity of the fluid

Step 2: Explore Stokes' Law

• Definition: Stokes' Law describes the force of viscosity exerted on a sphere moving through a viscous fluid.
• Formula: The law can be expressed as: [ F_d = 6 \pi \eta r v ] Where:
  • ( F_d ) is the drag force
  • ( \eta ) is the dynamic viscosity of the fluid
  • ( r ) is the radius of the sphere
  • ( v ) is the velocity of the sphere

Step 3: Derive the Terminal Velocity Formula

• Equilibrium Condition: At terminal velocity, the drag force equals the weight of the object.
• Weight of the Object: [ W = \frac{4}{3} \pi r^3 \rho g ] Where:
  • ( \rho ) is the density of the object
  • ( g ) is the acceleration due to gravity
• Set Forces Equal: [ 6 \pi \eta r v_t = \frac{4}{3} \pi r^3 \rho g ]
• Solve for Terminal Velocity: [ v_t = \frac{2r^2 (\rho g)}{9 \eta} ] This equation shows how terminal velocity depends on the radius of the object, the density of the fluid, and the viscosity of the fluid.

Step 4: Apply the Concepts with Examples

• Example Problem: Calculate the terminal velocity of a small sphere in a fluid.

  • Given:

    • Radius ( r = 0.01 ) m
    • Density of sphere ( \rho = 2500 ) kg/m³
    • Viscosity of fluid ( \eta = 0.001 ) Pa.s
    • Density of fluid ( \rho_{fluid} = 1000 ) kg/m³

  • Calculate: [ v_t = \frac{2(0.01)^2 (2500 \cdot 9.81)}{9 \cdot 0.001} ]

  • This calculation will yield the terminal velocity in meters per second.

Conclusion

In this tutorial, we covered the definition and factors influencing terminal velocity, explored Stokes' Law, derived the terminal velocity formula, and worked through an example problem. Understanding these concepts is crucial in various scientific and engineering applications related to fluid dynamics. For further study, consider experimenting with different variables in the terminal velocity formula to see how they affect the outcome.