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Terminal velocity

When any object rises or falls through a fluid it will experience a viscous drag, whether it is a parachutist or spacecraft falling through air, a stone falling through water or a bubble rising through fizzy lemonade.

Consider an object falling through a viscous fluid. As the object falls so its velocity increases but so does the drag on it due to the movement of the fluid past it. We call this the viscous drag.

As the object falls faster and faster the drag force increases. Eventually the drag force increases to a value where it is equal to the weight of the object and the body continues to fall at a steady speed. We call this the terminal velocity of the object. (shown by Figure 2).

For details of the mathematics of this force see: Stokes' Law
At this speed:

Viscous drag = Weight = mg

Large raindrops hurt much more than small ones when they fall on you - it's not just that they are heavier, they have a higher terminal velocity and so are actually falling faster.

People falling through the atmosphere will also eventually reach their terminal velocity. For low-level air (below about 3000 m) this is around 200 km/hour flat out and just over 320 km/hour head down. However at high altitudes around 30 000m this can reach almost 1000 km/hour!

Figure 3 shows how the velocity of an object will increase with time as it falls through a viscous fluid.


© Keith Gibbs 2020