Running Waters - Mathematics and Statistics for the Environment - page 561

19.4 TIME OF TRAVEL
Dye study or computation is used to determine the time of travel of running water. Running water
time of travel and river or stream geometry characteristics can be computed using a volume dis-
placement model. The time of travel is determined at any specific reach as the channel volume of
the reach divided by the flow as follows:

t = V / Q × 1/86,40 0 (19.3)

where
t = Time of travel at a stream reach (days).
V = Stream reach volume (ft 3 or m 3 ).
Q = Average stream flow in each (ft 3 /sec, cfs; m 3 /m).

■ EXAMPLE 19.2
Problem: The cross-section areas at river miles 63.5, 64.0, 64.5, 65.0, and 65.7 are, respectively,
270, 264, 263, 258, 257, and 260 ft 2 at a surface water elevation. The average flow is 32.3 cfs. Find
the time of travel for a reach between river miles 63.5 and 65.7.

Solution: Find the area in the reach:

Average area = 1/6(270 + 264 + 263 + 258 + 257 + 260) = 262 ft 2

Now find the volume:

Distance of the reach = 65.7 miles - 63.5 miles = 2.2 miles × 5280 ft/mile = 11,616 ft

Volume = 262 ft 2 × 11,616 ft = 3,043,392 ft 3

Now find time of travel ( t ):

V
Q

1
86 400

3 043 392
32 386 400

, ,

t =× = = 1.1 days

, . × ,

19.5 DISSOLVED OXYGEN
A running water system both produces and consumes oxygen. It gains oxygen from the atmosphere
and from plants as a result of photosynthesis. Running water, because of its churning, dissolves
more oxygen than does still water, such as that in a lake, reservoir or pond. Respiration by aquatic
animals, decomposition, and various chemical reactions consume oxygen. Dissolved oxygen (DO)
in running waters is as critical to the good health of stream organisms as is gaseous oxygen to
humans. Simply, DO is essential to the respiration of aquatic organisms, and its concentration in
streams is a major determinant of the species composition of biota in the water and underlying sedi-
ments. Moreover, DO in streams has a profound effect on the biochemical reactions that occur in
water and sediments, which in turn affect numerous aspects of water quality, including the solubil-
ity of many lotic elements and aesthetic qualities of odor and taste. For these reasons, DO histori-
cally has been one of the most frequently measured indicators of water quality (Hem, 1985).
In the absence of substances that cause its depletion, the DO concentration in running waters
approximates the saturation level for oxygen in water in contact with the atmosphere and decreases
with increasing water temperature from about 14 mg/L (milligrams per liter) at freezing to about
7 mg/L at 86°F (30°C). For this reason, in ecologically healthy streams, the DO concentration
depends primarily on temperature, which varies with season and climate.