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24 3

Re jRe

where Re is the Reynolds number = vpwd/f, and f is the dynamic viscosity of water. Values of Re less than 1 indicate laminar flow, while values greater than 104 indicate turbulent flow. Intermediate values indicate transitional flow.

Substituting the CD for laminar flow (CD = 24/Re) in Equation (5.11), produces the Stokes equation:

To use the previous equations for non-spherical particles, the diameter d, must be the diameter of the equivalent spherical particle. The volume of the equivalent spherical particle Vs = 3 n(2)3, must be equal to the volume of the non-spherical particle Vp = ¡¡dp,, where f is a volume shape factor. Expressing the equality and solving for the equivalent spherical diameter d produces d = n P1" dP (5.16)

The following values of sand volumetric shape factors ¡ have been reported: angular = 0.64, sharp = 0.77, worn = 0.86, and spherical = 0.52.

Example 5.3 Determine the terminal settling velocity of a spherical particle having a diameter of 0.6 mm and specific gravity of 2.65. Assume the settling is type 1 and the temperature of the water is 22°C.

Solution:

d = 0.6( 10-3) m fi22 = 9.2 (10-4) kg/m-s = 9.2( 10-4) N-s/m2

Therefore,

4 ( [2650-997] [0:6(10:.)] = 0.114 3( . j C»(997) C

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