Why Don’t Clouds Fall?

When I gaze at these masterpieces created by Mother Nature, I often find myself wondering: if clouds contain water, which is heavier than air, how do these enormous, fluffy sky giants manage to stay aloft instead of falling to the ground? It’s a fascinating question, isn’t it? Today, I’ll give you an answer that blends science with curiosity.

Clouds can be made up of tiny droplets of liquid water or small crystals of solid water—but not water vapor. Water vapor is the gaseous form of water, which is invisible, colorless, and completely transparent. But let’s set aside vapor for now and focus on clouds as we see them.

To understand why a cloud remains suspended in the sky and doesn’t fall, we need to consider the forces acting on it. Imagine an ideal scenario: let’s assume there are no significant air currents (no wind) and that the flow is laminar—smooth and without turbulence. In this situation, we can identify three main forces acting on our “little cloud”:

Gravitational Force

F_g = m g

• F_g: Gravitational force (in newtons, N)
• m: Mass of the object (in kilograms, kg)
• g: Acceleration due to gravity (9.81 m/s²)

Buoyant Force

F_b = ρ_air V g

• F_b: Buoyant force (in newtons, N)
• ρ_air: Density of air (in kilograms per cubic meter, kg/m³)
• V: Volume of the object (in cubic meters, m³)
• g: Acceleration due to gravity (9.81 m/s²)

Drag Force

F_d = 6π η r v

• F_d: Drag force (in newtons, N)
• η: Dynamic viscosity of air (in pascal-seconds, Pa·s)
• r: Radius of the droplet (in meters, m)
• v: Velocity of the droplet (in meters per second, m/s)

Our goal is to determine whether these forces balance each other or if the cloud actually falls. To do this, we calculate its “hypothetical” terminal velocity: the speed at which all the forces cancel out, resulting in no further acceleration.

To calculate this terminal velocity, we need a few key parameters:

• The density of air and water.

• The viscosity of air.

• The radius of a single water droplet that makes up the cloud.

Each droplet in a cloud typically measures between 5 to 50 microns (μm\mu mμm) in diameter, a scale that profoundly influences their behavior under physical forces

Terminal Velocity

v_t = (2/9) × [r² × (ρ_water - ρ_air) × g] / η

• v_t: Terminal velocity (in meters per second, m/s)
• r: Radius of the droplet (in meters, m)
• ρ_water: Density of water (in kilograms per cubic meter, kg/m³)
• ρ_air: Density of air (in kilograms per cubic meter, kg/m³)
• g: Acceleration due to gravity (9.81 m/s²)
• η: Dynamic viscosity of air (in pascal-seconds, Pa·s)

Plugging these values into the formula, we get an intriguing result. The terminal velocity of water droplets is incredibly small: just 0.01 m/s, or 1 cm per second. At this speed, even though clouds technically “fall,” their motion is so slow that to the naked eye, they appear to float effortlessly in the sky.

But there’s more! This is just part of the story. Air currents and turbulent motions, which we ignored in this simplified scenario, play a crucial role in keeping clouds aloft and shaping their forms and movements.

Next time you look up at a cloud, think about this delicate dance of invisible forces that keeps it suspended and makes the sky a stage for ever-changing beauty.

VIDEO

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