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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:
16-19/Properties of matter/Viscosity/Text/Stokes law
Figure 1
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.
Velocity of
falling sphere
Terminal velocity
Figure 3
Viscous drag
m
Velocity v
Gravitational pull (weight) mg
Figure 2