Example Problem III-1-3 (Concluded)

c) The fall velocity is read from Figure III-1-6 as 150 cm/sec. *Re *is calculated from its

definition as:

This agrees reasonably well with Figure III-1-5.

d) Expecting to find Re < 0.5, Equation 1-9 can be used to find *W*f.

From its definition:

Thus, use of Equation 1-9 is well justified. From Equation 1-8:

e) Estimating that *Re *will be in the range 400 < *Re *< 200,000, Equation 1-10 can be used to find

an estimate of *W*f.

Thus, use of Equation 1-10 is justified. From Figure III-1-5, it is seen that a CD value of 0.4 is better

than the value of 0.5 used in Equation III-1-10. Iterating using this value in Equation 1-7 yields:

Alternatively, Equation III-1-12 could have been used to obtain:

π/8 *C*D Re2 = 3.14*(0.45)3*(7.8/0.0012-1)*980/(6 * (0.15)2)=1.3x107

Using Figure III-1-5, this yields similar values of 12,000 and 0.4 for *Re *and *C*D, respectively.

f) It is important to realize that this particle is lighter than water and its direction of motion will be

upward. This is implied in the result by the fall velocity having a negative value. Estimating that *Re *will

be in the range *Re *> 200,000, Equation 1-11 can be used to find an estimate of *W*f.

Thus, use of Equation 1-11 is justified. Alternatively, Equation 1-12 could have been used to obtain:

π/8 *C*D Re2 = 3.14*(16.5)3*(0.48/1-1)*980/(6 * (0.011)2)=(-)9.9x109

Using Figure III-1-5, this yields similar values of 4x105 and 0.2 for *Re *and *C*D, respectively.

Coastal Sediment Properties

III-1-29

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