EM 1110-2-1100 (Part III)
30 Apr 02
(11) The transition between the second and third regime corresponds to approximately 90-mm quartz
spheres (cobbles, as shown on Table III-1-2) falling in water.
(12) Generally for grain sizes outside the range shown in Figure III-1-6 or for spheres with a density
other than quartz, or fluids other than air or water, Equation 1-7 can be used with a value of CD obtained from
Figure III-1-5. However, this is an iterative procedure involving repeated calculations of fall velocity and
Reynolds number. Instead, Equation 1-7 can be rearranged to yield:
CD Re 2 '
This quantity, π/8 CD Re2 , can be used in Figure III-1-5 to obtain a value of CD or Re , either of which can
then be used to calculate the fall velocity.
b. Effect of density. Equation 1-7 shows that fall velocity depends on ((ρs /ρ)-1). For quartz sand
grains in fresh water, this factor is about 1.28. For quartz grains in ocean water, this factor reduces to about
1.25 because of the slight increase in density of salt water. For quartz grains in very turbid (muddy) water,
the factor will decrease somewhat more. If the suspended mud is present in a concentration of 10 percent by
mass, ((ρs /ρ)-1) becomes 1.19. Thus, natural increases in water density encountered in coastal engineering
will decrease the fall velocity of quartz by not much more than (1.28 - 1.19) / 1.28 = 0.07, or on the order of
c. Effect of temperature. Temperature has an effect on the density of water; however, this is very small
compared to its effect on the coefficient of viscosity. Changes in the fluid viscosity affect the fall velocity
for small particles but not for large. (Equation 1-8 contains a viscosity term while Equations 1-9 and 1-10
do not.) Figure III-1-6 has separate lines labeled with temperatures of 0E, 10E, 20E, 30E, and 40 EC, and these
lines are reversed for the two fluids. A grain will fall faster in warmer water, but slower in warmer air,
compared to its fall velocities at lower temperatures. This difference is the direct result of how viscosity
varies with temperature in the two fluids.
d. Effect of particle shape.
(1) Grain shape affects the fall velocity of large particles (those larger than Re about 10 or D about 0.125
mm in water) but has a negligible effect on small particles. For large grains of a given nominal diameter, the
less spherical the particle, the slower the fall velocity. In Figure III-1-5 it is seen that at large Reynolds
numbers, discs have higher CD values, and thus lower fall velocities than spheres.
(2) Mehta, Lee, and Christensen (1980) investigated the fall velocity of natural shells (unbroken bivalve
halves). For Re in the range of 1,000-5,000, they found that if the shells rocked but did not spin as they fell,
CD values ranged from about 0.7 to 1.0 depending upon a shape factor. The less spherical, the greater the
drag. If the shells spun while falling, the drag coefficient increased to the range of 1.0 to 1.5. For large
particles that are far from spherical, it is usually best to determine their fall velocity experimentally.
Coastal Sediment Properties