Environmental Engineering Reference
In-Depth Information
because the water encounters more friction while flowing through the
smaller pores.
If we put the equations for inertia and viscosity together and cancel,
we get the equation for Reynolds number:
SU
2
F
i
F
v
U l
Re
l
U
The Reynolds number is greater at large spatial scales (a large fish) than at
small scales (a bacterium or protozoan) (Fig. 2.6). Calculations of this
number (Example 2.1) reveal the wide variations in viscosity experienced
between large and small organisms. A summary of the effects of scale re-
lated to Re is provided in Table 2.3. Reynolds numbers will be considered
again when I discuss filter feeding of lake and stream organisms, microbial
food webs, production of aquatic macrophytes, and flow of water in
streams and groundwaters.
MOVEMENT OF WATER
At the very smallest scale, molecules move independently in the process
called
Brownian motion
. The warmer the water, the more rapidly the mol-
ecules move. The average instantaneous velocity of individual water mole-
cules is extremely rapid (
100 m s
1
), but because they continuously col-
lide, individual molecules move from any location slowly (50
10
9
m
s
1
, Denny, 1993).
EXAMPLE 2.1.
Reynolds Number Calculations
Calculate viscous force (
F
v
), inertia (
F
i
), and Reynolds (Re) number for two
cubes, one 1
m and the second 1 cm on a side, each moving at 2 lengths
per second, given that
10
6
g m
3
1 g m
1
s
1
. If tur-
1
and
bulent flow is more likely to occur above Re
100, which cube would
have its hydrodynamic properties altered more by streamlining?
Parameter
Comment
1-cm cube
1-
m cube
10
2
10
6
L
Length of cube
m
m
10
4
m
2
10
12
m
2
S
Square of length
10
2
m s
1
10
6
m s
1
U
Two lengths per second
2
2
10
2
g m s
2
10
18
g m s
2
F
i
From equation
4
4
10
4
g m s
2
10
12
g m s
2
F
v
From equation
2
2
10
6
Re
F
i
/
F
v
200
2
Note that inertia is very, very small for the small cube, leading to a
much smaller Reynolds number. The 1-cm cube is above Re
100 and its
hydrodynamic properties would be altered more than those of the 1-
m
cube if both were streamlined.
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