Mean stream slope

Fig. 1 Results from a redundancy analysis of stream nutrient concentrations vs. catchment characteristics in 31 headwater catchments in Catalonia (Spain). Note how phosphorus (SRP) and ammonium (NH4) appear associated with urban point and diffuse sources (Urban percent urban land use, Inhabs number of inhabitants, eq. inhab inhabitant equivalents), whereas nitrate (NO3) concentration is positively associated with irrigated agriculture (IrrAg) and bovine cattle units (ECU), and negatively with mean catchment slope (slope) and percent forest land (Forest). The other variables are Area log area, P precipitation, NonIrrAg non irrigated agriculture. Data are from the Catalan water agency (http //ww.gencat.cat/ac)...

In this reach, on the day of the spill, the Maipo River carried a discharge of 60 m /s, at a mean depth of 2 m, with a mean cross-sectional area of 60 m2 and a stream slope of 0.002. The longitudinal dispersion coefficient is known to be 20 m2/s. 

Moog and Jirka also found that Equation 9.29, even though it was the best predictor, still had a mean multiplicative error of 1.8. This means that one can expect the predictions of Equation 9.29 to be off the field measurements by either multiplying or dividing by a factor of 1.8. Fifty percent of the predictions will differ by more than this factor, and 50% by less. In addition, they found that below a stream slope of... 

FIGURE 9.14 Measurements of liquid film coefficients for field streams versus bottom shear velocity, m = /gHS, where g is acceleration of gravity, H is mean stream depth, and S is stream slope. An exponential curve is fit through the data. (Data from Moog, D. B. and Jirka, G. H. 1998. J. Environ. Eng., 124(2), 104.)... 

Levenspiel and Smith Chem. Eng. Sci., 6 (227), 1957] have reported the data below for a residence time experiment involving a length of 2.85 cm diameter pyrex tubing. A volume of KMn04 solution that would fill 2.54 cm of the tube was rapidly injected into a water stream with a linear velocity of 35.7 cm/sec. A photoelectric cell 2.74 m downstream from the injection point is used to monitor the local KMn04 concentration. Use slope, variance, and maximum concentration approaches to determine the dispersion parameter. What is the mean residence time of the fluid ... 

Now, consider a natural river, illustrated in Figure 9.3. There are many sources of vorticity in a natural river that are not related to bottom shear. Free-surface vortices are formed in front of and behind islands and at channel contractions and expansions. These could have a direct influence on reaeration coefficient, without the dampening effect of stream depth. The measurement of p and surface vorticity in a field stream remains a challenge that has not been adequately addressed. The mean values that are determined with field measurements are not appropriate. Most predictive equations for reaeration coefficient use an arithmetic mean velocity, depth, and slope over the entire reach of the measurement (Moog and Jirka, 1998). The process of measuring reaeration coefficient dictates that these reaches be long to insure the accuracy of K2. Flume measurements, however, have generally shown that K2 u /hor K2 (Thackston and Krenkel, 1969 ... 

The difference between the two means is a factor of 2.2. This value is larger than the expected error of equation (9.7). Thus, a channel with a variation in slope and cross section along its length will have a higher K2 value computed from arithmetic means than an otherwise equivalent channel that does not have variation in slope and cross section. It may not be a coincidence that Moog and Jirka s calibration of Thackston and Krenkel s equation for flumes is an adjustment by a factor of 0.69 to represent held measurements. We need to pay attention to the impact that these variations in natural rivers and streams have on our predictive equations for K2. 

FIGURE 3 Relationships between annual runoff and watershed export of DOC in streams and rivers reported in the literature. The respective lines extend only over the range of runoff values included in the dataset. The slopes of each line are approximately equivalent to the mean annual DOC concentration for that group (in parentheses). Sources for each relationship are as follows streams with wetlands, temperate (Mulholland, 1997) streams with wetlands, N. Carolina (Mulholland and Kuenzler, 1979) large rivers, global (Spitzy and Leenheer, 1991) large rivers, N. America (Mulholland and Watts, 1992) streams, tropical (McDowell and Asbury, 1994) streams, N. America (Mulholland, 1997). 

In the case of pressure conduits, we have dealt with uniform and nonuniform flow without drawing much distinction between them. This can be done because in a closed pipe the area of the water section, and hence the mean velocity, is fixed at every point. But in an open channel these conditions are not fixed, and the stream adjusts itself to the size of cross section that the slope of the hydraulic gradient requires. 

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