High-Reynolds-number flows

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Since the air (and water) viscosity is small, in many flows encountered in everyday life the Reynolds number Re is very large. The two most common fluids are air and water. The Reynolds number Re = U L /ν depends on the fluid kinematic viscosity ν, which is the property of the fluid, and the characteristic velocity U and the characteristic length L.

The following table gives several examples of the values of Re for particular values of the speed and length for air and water.

Size L Speed U Re in air (at 20 C) Re in water (at 20 C)
1 cm 1 cm/sec 7  102
1 m 1 m/sec 66,200 1.02×106
10 m 10 m/sec 6.62×106 1.02×108

Note that Re in water is roughly 15 times higher than Re in air for the same characteristic length and speed.

The second table shows the typical values of the Reynolds number for various applications.

Bacterium Re ∼ 0.000,01
Blood flows 0.002 < Re < 2,000
Housefly Re ∼ 100
Big butterfly Re ∼ 4,000
Large fish or large bird Re ∼ 50,000
Person running Re ∼ 500,000
Cars 5×106 < Re < 6×107
Aircraft 3×107 < Re < 8×108
Ship 5×107 < Re < 5×109
Atmospheric flows Re > 109

Hence, flows at large Reynolds numbers deserve a special attention.

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