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When a sphere of radius r1 = 1.2 mm moves through glycerin, the flow stays laminar provided its speed does not exceed v1 = 23 cm/s. Using the idea that the flow turns turbulent at the same value of Reynolds number, find the minimum speed v2 of a sphere of radius r2 = 5.5 cm at which flow in water becomes turbulent. Viscosity of glycerin eta1 = 13.9 P, viscosity of water eta2 = 0.011 P, density of glycerin = 1.26 g/cc (use density of water = 1.0 g/cc).
- 0.23 cm/s
- 2.3 cm/s
- 23 cm/s
- 230 cm/s
Correct answer: 0.23 cm/s
Solution
The transition to turbulence happens at the same critical Reynolds number. Writing Re = rho*v*(2r)/eta for both fluids and equating them lets you solve for v2 in terms of the given quantities. Substituting the densities, radii, and viscosities yields v2 ~ 0.23 cm/s.
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