MadSci Network: Earth Sciences Query:

### Re: How does gravity affect the speed of a raindrop?

Date: Wed May 23 09:53:08 2001
Posted By: Nezette Rydell, forecaster,National Weather Service
Area of science: Earth Sciences
ID: 989630895.Es
Message:

```Two forces act on a falling raindrop.  The Earth's gravitational force is a
downward acting force and the force exerted by the air (frictional
resistance) is an upward acting force.

Earth's gravity pulls objects downward at a constant rate, 9.8 meters per
second each second ( 9.8 meters per second squared).  The raindrop's fall
will accelerate (or speed up) until the gravitational force is equal
to the force of the air pushing up against it.  The net force on the
raindrop is then zero and according to Newton's second law, the drop
stops accelerating and continues to fall at a constant speed.  This speed
is called the terminal velocity.

The terminal velocity depends on the size of the raindrop.  Smaller
droplets have lower terminal velocities.  (The smallest drops, cloud
droplets, are suspended in the atmosphere and do not fall.)  The upward
force exerted on the raindrop is proportional (directly related) to the
cross-sectional area of the raindrop.  If the raindrop is round,
then its area is given by the area of a sphere, ( (pi) times (the radius of
the raindrop squared) ).  The downward force is proprotional to the
volume of the sphere, ( (4/3 pi) times (radius of the raindrop
cubed) ).  For larger drops, the downward force changes more, at a cubic
rate, while the upward force changes less, at a squared rate.  The downward
force on the raindrop is greater with larger raindrops.

In reality, raindrops are not round.  The smallest cloud droplets are
indeed spheres.  Larger drops are distorted by the upward force and are
essentially squashed as they fall, becoming flat on the bottom.  A
great little book about raindrops and other stuff is
From Raindrops to Volcanoes:  Adventures in Sea Surface Meteorology by
Duncan Blanchard.  It is out of print but can be found in libraries and
used book stores.

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