Terminal Velocity & Stokes Law | Physics for JAMB PDF Download

Qualitative Treatment of Viscosity and Terminal Velocity

1. Factors that affect viscosity:

• Temperature: Viscosity generally decreases with an increase in temperature. As temperature rises, the kinetic energy of the molecules increases, leading to weaker intermolecular forces and reduced viscosity.
• Molecular size and shape: Longer and more complex molecules tend to have higher viscosities due to increased intermolecular forces and greater resistance to flow.
• Intermolecular forces: Stronger intermolecular forces, such as hydrogen bonding, increase viscosity by hindering molecular motion.
• Pressure: Viscosity tends to increase with higher pressure due to closer packing of molecules and enhanced intermolecular forces.

2 Factors that affect terminal velocity:

• Mass and size of the object: Larger or more massive objects experience higher drag forces, resulting in a lower terminal velocity.
• Shape of the object: Objects with streamlined shapes experience less air resistance and attain higher terminal velocities compared to objects with irregular shapes.
• Density of the medium: Terminal velocity is influenced by the density of the fluid through which the object is moving. Higher density fluids offer greater resistance, reducing the terminal velocity.

Stoke's Law

Stoke's law describes the motion of small spherical particles falling through a viscous medium. According to Stoke's law, the drag force (F) acting on a small spherical particle moving through a viscous medium is given by:
F = 6πηrv
Where:

• F is the drag force
• η is the viscosity of the medium
• r is the radius of the particle
• v is the velocity of the particle relative to the medium

Stoke's law assumes laminar (non-turbulent) flow conditions and is valid for low Reynolds numbers. It provides a linear relationship between the drag force and the velocity of the particle.

Application of Stoke's law

Stoke's law can be applied to determine the terminal velocity (v_t) of a small spherical particle falling through a viscous medium. When the drag force becomes equal to the weight of the particle (mg), the particle reaches a state of equilibrium, and its velocity no longer increases. At this point, the particle's terminal velocity can be calculated using the equation:
mg = 6πηrv_t
By rearranging the equation, the terminal velocity can be determined as:
v_t = (2/9)(g/η)r²
Where:
g is the acceleration due to gravity
Stoke's law is commonly used in the study of fluid dynamics, sedimentation, and particle analysis.