What is Stokes' Law?

S4-SA1-0839

Grade Level:

Class 8

Space Technology, EVs, Climate Change, Biotechnology, HealthTech, Robotics, Chemistry, Physics

Definition

What is it?

Stokes' Law helps us calculate the drag force (resistance) that a small, spherical object experiences when it moves through a liquid or gas. It tells us that this drag force depends on the object's size, its speed, and how thick (viscous) the fluid is.

Simple Example

Quick Example

Imagine a small pebble falling through a bucket of water. It falls slower than it would in air because water is thicker. Stokes' Law helps us understand exactly how much slower it falls due to the water's resistance. If you drop a tiny steel ball into honey, it would fall even slower because honey is much thicker than water.

Worked Example

Step-by-Step

Let's calculate the drag force on a tiny dust particle falling through air. --- 1. Identify the given values: Radius (r) of the dust particle = 0.00001 meters (10 micrometers). Speed (v) of the dust particle = 0.001 meters/second. Viscosity (η) of air = 0.000018 Pascal-seconds (a measure of its thickness). --- 2. Recall Stokes' Law formula: F_d = 6 * pi * η * r * v. --- 3. Substitute the values into the formula: F_d = 6 * 3.14 * 0.000018 * 0.00001 * 0.001. --- 4. Multiply the numbers: F_d = 0.0000000000033912 Newtons. --- Answer: The drag force on the dust particle is approximately 3.39 x 10^-12 Newtons.

Why It Matters

Stokes' Law is crucial in fields like climate change, helping scientists understand how tiny dust or pollutant particles move in the atmosphere. It's also used in biotechnology to separate cells and in healthtech for designing drug delivery systems. Engineers in robotics use it to design machines that move through fluids efficiently.

Common Mistakes

MISTAKE: Confusing drag force with gravity. | CORRECTION: Drag force is the resistance from the fluid, acting opposite to motion. Gravity is the force pulling the object down. These are different forces.

MISTAKE: Forgetting that Stokes' Law applies mainly to small, spherical objects moving slowly. | CORRECTION: Stokes' Law has limitations. It's most accurate for laminar flow (smooth flow) around small spheres, not for large, irregularly shaped objects or very fast movements.

MISTAKE: Using incorrect units for viscosity or radius. | CORRECTION: Always ensure all measurements (radius, velocity, viscosity) are in standard SI units (meters, meters/second, Pascal-seconds) before applying the formula.

Practice Questions

Try It Yourself

QUESTION: A tiny glass bead with a radius of 0.00005 meters falls through oil with a viscosity of 0.1 Pascal-seconds at a speed of 0.0002 meters/second. Calculate the drag force on the bead (use pi = 3.14). | ANSWER: F_d = 6 * 3.14 * 0.1 * 0.00005 * 0.0002 = 0.00000001884 Newtons or 1.884 x 10^-8 Newtons.

QUESTION: If the drag force on a spherical pollen grain moving through air is 6 x 10^-12 Newtons, its radius is 0.00002 meters, and air viscosity is 0.000018 Pascal-seconds, what is the speed of the pollen grain? (Use pi = 3.14). | ANSWER: v = F_d / (6 * pi * η * r) = 6 x 10^-12 / (6 * 3.14 * 0.000018 * 0.00002) = 6 x 10^-12 / 0.0000000067824 = 0.0008846 meters/second.

QUESTION: Two identical small marbles fall through two different liquids. Liquid A has a viscosity of 0.05 Pascal-seconds, and Liquid B has a viscosity of 0.2 Pascal-seconds. If both marbles fall at the same speed, what is the ratio of the drag force in Liquid B to the drag force in Liquid A? | ANSWER: F_d is directly proportional to viscosity. So, F_dB / F_dA = η_B / η_A = 0.2 / 0.05 = 4. The ratio is 4:1.

MCQ

Quick Quiz

Which factor does NOT directly affect the drag force according to Stokes' Law?

Radius of the object

Speed of the object

Density of the object

Viscosity of the fluid

The Correct Answer Is:

Stokes' Law (F_d = 6 * pi * η * r * v) shows that drag force depends on viscosity (η), radius (r), and speed (v). The density of the object is not directly part of the Stokes' Law formula for drag force.

Real World Connection

In the Real World

Stokes' Law helps scientists at ISRO understand how tiny dust particles behave in the upper atmosphere or on other planets like Mars. It's also used in pharmaceutical companies to control how tiny medicine particles move through liquids, ensuring the correct dosage and absorption in the human body. Even in water purification plants, understanding how small impurities settle is linked to this principle.

Key Vocabulary

Key Terms

DRAG FORCE: The resistance force experienced by an object moving through a fluid. | VISCOSITY: A measure of a fluid's 'thickness' or resistance to flow. | SPHERICAL: Having the shape of a sphere or ball. | FLUID: A substance that can flow, like a liquid or gas. | LAMINAR FLOW: Smooth, orderly flow of a fluid around an object.

What's Next

What to Learn Next

Great job understanding Stokes' Law! Next, you can explore 'Terminal Velocity'. This concept builds on Stokes' Law by explaining why a falling object eventually reaches a constant speed when the drag force balances gravity. Keep up the amazing work!