Hey Future Physicist! 🎓 Grab a drink (but not too viscous!) and let's dive into the cool world of fluids, drag, and spheres moving through them. We're talking about George Stokes' law, who was a cool Irish scientist from way back in 1851. Ready? Let's get moving!

Stokes' law helps us understand how things move in fluids like water, honey, or even air. Imagine trying to swim through a pool of honey; it's going to be a sticky situation. That's what this law explains!

Key Concepts

• Viscosity: It's like the "thickness" of the fluid. Honey has high viscosity (pours slowly) and water has low viscosity (pours quickly).
• Drag Force: Imagine wearing a parachute and trying to run. The air pulls you back, and that's drag. Stokes calculated the drag force (Fd) on a sphere in a fluid as Fd=6πηrv, where:
• r: radius of the sphere
• v: speed of the sphere
• η: dynamic viscosity of the fluid (e.g., 1×10−3 Pa s1×10−3Pa s for water and up to 20 Pa s20Pa s for honey).
• Temperature Dependence: Just like how butter melts on a hot pan, viscosity changes with temperature too!
• Laminar vs. Turbulent Flow: Imagine a calm river vs. wild rapids. Stokes' law only applies to calm, smooth flow (laminar). Real life is often more turbulent (swirly)!

• Flow is calm and smooth (laminar).
• Particles are perfect smooth spheres.
• The fluid is the same all the way through (homogeneous).
• Particles don't interact.

Think of dropping a tennis ball in a giant glass of water. Here are the forces at play:

• Weight (W): Gravity pulling down on the ball.
• Buoyancy (B): The "floaty" force pushing up. Given by B = ρf​gV, where ρf​ is the fluid's density and V is the sphere's volume.
• Drag (D): The sticky, slow-down force going up, calculated using Stokes' law.

The net force is W−B−DW−B−D, and it can also be expressed as (ρs​ − ρf​)gV−6πηrv, where ρs​ is the sphere's density.

The ball will keep speeding up until drag and buoyancy balance the weight. Then it reaches a constant speed called terminal speed, given by vt = 6πηr (ρs​−ρf​)gV​.