### Question

Why is it, that if you lower your hand flat into, say, a pool there is no or hardly any resistance but if you were to raise your hand and slap it down hard into the water, there is so much resistance?

For much the same reason you can stick your hand out of the window of a car moving at 5 mph with very little difficulty, but risk injury if you try the same thing at 100 mph. The resistance that a fluid (air, in this example) offers to an object (your hand) moving through it is determined by, among other things, the speed of the object. That resistance increases with the SQUARE of the speed, so just doubling the speed increases fluid resistance FOUR times.

In the moving car example above, increasing speed from 5 mph to 100 mph increases air resistance by a factor of 100/5 SQUARED, or 400 times. So a force on your hand of 1 pound at 5 mph becomes 400 pounds at 100 mph. Going from a gentle motion to a slap on the surface of a pool is another illustration of the effect speed has on fluid resistance.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor

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