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 LSpeed URe in air (at 20 C)Re in water (at 20 C)
1 cm1 cm/sec7 102
1 m1 m/sec66,2001.02×106
10 m10 m/sec6.62×1061.02×108

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.

BacteriumRe ∼ 0.000,01
Blood flows0.002 < Re < 2,000
HouseflyRe ∼ 100
Big butterflyRe ∼ 4,000
Large fish or large birdRe ∼ 50,000
Person runningRe ∼ 500,000
Cars5×106 < Re < 6×107
Aircraft3×107 < Re < 8×108
Ship5×107 < Re < 5×109
Atmospheric flowsRe > 109

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

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