Rivers travel time

The travel time for suspended load is controlled by the flow velocity and the distance to the basin outlet. Flow velocities do not change much downstream in a typical river system (Leopold, 1953) and typically range from 0.1 to several m/s. Hence, suspended load should be able to travel at least 10 to 100 km per day and the travel time for suspended sediment to traverse even the longest rivers in the world should be less than a season. Although some of the suspended load will be deposited in floodplains, the component of the suspended load that does not get sequestered in terrestrial depositional environments is delivered almost as fast as the water that it flows in. Bedload travels much more slowly. In mountain drainage basins, the velocity of individual bedload clasts is on the... 

Now—the now that is a time beyond the confines of this story, a now in which this story is past—I do not worry the past as I did then. Now it is set for me in a way that it was not set then. Not set then because so recent, still to be relived in memory and learned from. Five days of river travel lay before us—undemanding, freeing the mind to rove and scan. 

After a fire in a chemical storehouse at Schweizerhalle, Switzerland, in November 1986, several tons of various pesticides, solvents, dyes, and other raw and intermediate chemicals were flushed into the Rhine River (Capel et al., 1988 Wanner et al., 1989). Among these chemicals was the insecticide disulfoton, of which 3500 kg were introduced into the river water (11°C, pH 7.5). During the 8 days travel time from Schweizerhalle to the Dutch border, 2500 kg of this compound were eliminated from the river water. Somebody wants to know how much of this elimination was due to abiotic hydrolysis. Since in the literature you do not find any good kinetic data for the hydrolysis of disulfoton, you make your own measurements in the laboratory. Under all selected experimental conditions, you observe (pseudo)first-order kinetics, and you get the results given below. 

Check whether the assumption of vertical and lateral homogeneity from the point of tracer injection to the first cascade (1 km downstream) is justified. At the start of the injection, a short pulse of uranin (sodium fluorescein, a fluorescent dye) was added to the river in order to measure the travel time of the water. At each station, the samples for analyzing the halogenated compounds were taken 1.5 hours after the uranin peak had passed by. Based on this information, justify why longitudinal dispersion can be disregarded in the evaluation of the experiment. 

Note that A is less than the mean advective traveling time from the river to the well, tw = 2.4 d (for Pump Regime II). The table below summarizes the relevant parameters for all periods and pump regimes. 

Changes in the water table of the Mohawk River and a number of adjacent observation wells is reported in Fig. 4.10, adapted from Winslow et al. (1965). The wells followed the river, with a time lag of 4-12 hours (insert in Fig. 4.10). Two possible explanations for this time lag may be envisaged (1) arrival of the hydraulic pulse, or (2) arrival of the recharge front (assuming piston flow section 2.1). To tell the two apart, the time lag observed for these wells by temperature measurements is helpful, as discussed in section 4.8 (see Fig. 4.21). The temperature time lag of, for example, well 58, has been observed to be about 3 months, whereas the water table time lag was only 12 hours. The latter defines the arrival of the hydraulic pulse, whereas the former defines the travel time of the recharge front. The distances given in the insert in Fig. 4.10, divided by the respective time lags, provided the... 

When a mass of a chemical is released at a point in a river, the center of the chemical s mass moves downstream at the average velocity of the river (Fig. 2-4, upper panel). The average amount of time it takes a chemical to travel from an upstream point to a downstream point in a river (i.e., to traverse the length of a given segment, or reach, of river) is called the travel time, r, and is expressed as... 

An estimate of travel time is important in many situations. For example, a municipal water supply operator needs to know how long it will take a chemical spilled upriver to reach downstream water intake pipes so that the valves can be closed before the spilled chemical arrives. An estimate of travel time is also necessary when calculating whether processes such as loss to the air (volatilization) or bacterial degradation will significantly decrease a chemical concentration along a reach of river. 

FIGURE 2-4 Transport of a chemical in a river. At time zero, a pulse injection is made at a location defined as distance zero in the river. As shown in the upper panel, at successive times C, t2, and t3, the chemical has moved farther downstream by advection, and also has spread out lengthwise in the river by mixing processes, which include turbulent diffusion and the dispersion associated with nonuniform velocity across the river cross section. Travel time between two points in the river is defined as the time required for the center of mass of chemical to move from one point to the other. Chemical concentration at any time and distance may be calculated according to Eq. [2-10]. As shown in the lower panel, Cmax, the peak concentration in the river at any time t, is the maximum value of Eq. [2-10] anywhere in the river at that time. The longitudinal dispersion coefficient may be calculated from the standard deviation of the concentration versus distance plot, Eq. [2-7]. 

For example, to estimate DL, a pulse of tracer is injected into a river and the longitudinal distribution of the tracer is measured as the river carries it past a downstream location. The spatial standard deviation of tracer and the travel time are determined from tracer concentration data, and DL is computed using Eq. [2-7]. 

To estimate the dispersion coefficient, consider the concentration profile at time t3 the peak of the profile (Cmax) occurs at approximately 1975 m, and the standard deviation is roughly 350 m. Assuming the average river velocity is 205 m/hr, the travel time to L3, using Eq. [2-3a], is... 

A stream is in equilibrium with atmospheric oxygen upstream of a waste outfall, which creates a BOD0 of 20 mg/liter immediately downstream. KBOD is 0.4/day, and KQ2 is 1.4/day. The stream temperature is 15°C. How far downstream, in terms of travel time, is the maximum DO sag, and what is the minimum DO in the river ... 

With an estimate of the veloeity at hand, a first approximation can be made to the time of travel between various points on the river. For example, the travel time, in days, to eover a given distance, in miles, can be estimated by knowing the velocity in miles per day. This relationship ignores dispersion or mixing in the river and any effects of dead zones such as deep holes or side channel coves. 

The fact that the pattern of silica variation in Conklin Creek is very similar to that in the Mattole River, even though the stream basins are different by a factor of about 40 in size, indicates that the observed variation in the Mattole basin is not owing to travel time effects. 

During a spill where the travel time is as long as that here, potential for unsteadiness of the river flow exists. If appreciable unsteadiness were expected, e.g., due to heavy rains, the best way to proceed would generally be to use a numerical model, such as the MIT model (75), or similar ones. Of course, a conservative estimate of concentrations can be made by neglecting the expected additional dilution. However, account would have to be taken of the decreased time of travel to downstream locations of interest, for example, fish hatcheries or water intakes. Not only would the material reach those points faster at higher flows, but the decreased time would result in less decay for nonconservative substances. 

For any planning of an oil spill into rivers or streams, a field investigation needs to be undertaken. This investigation involves determining the travel time of the reach, the longitudinal dispersion coefficient of the reach, and the gas transfer coefficient of the reach. An... 

It is interesting that four St. Clair River samples appear to be considerably above the normal range of data scatter while one Niagara River sample appears to be well below the scatter. These results may provide information on the time required to reach chemical equilibrium between the dissolved and particulates fractions. The fou r St. Clair River samples were collected at Port Lambton which is about 35 km and 10 hr travel time for the water below the major chemical sources at Sarnia. Much of the contaminants enter the St. Clair River in the particulate phase ( puddles of waste material have been found in the river. Environment Canada and Cntario Ministry of the Environment 1986) and may not have had sufficient time to reach equilibrium with the dissolved phase by the time the water reaches Port Lambton. Even higher partition coefficients have been observed in samples collected in industrial plumes near... 

Travel time and the longitudinal Fickian transport coefficient can also be evaluated from a continuous injection experiment, in which injection of tracer is initiated at time f=0 at a rate sufficient to establish a chemical concentration Co at the point of injection. Such an experiment is discussed for groimdwater in Section 3.2.5 the equation describing concentrations resulting from a continuous injection in a river is conceptually identical to Eq. (3.18). Equivalently, the injection of tracer can be described as mass per cross-sectional area per imit time (M), in which case the equation presented in the upper middle panel of Fig. 3.19 can also be used for a river, with porosity n equal to 1. 

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