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11.4
Factors Affecting Stream Flow
    Key Points
  1. • Stream gradient is the change in elevation of a stream over a given distance.
  2. • Stream gradient normally decreases in the downstream direction.
  3. • The average stream flow velocity increases downstream.
  4. • Stream discharge is the volume of water flowing through a stream.

Think for a moment about the last time you saw a stream or river. How would you describe that river to a friend? Chances are you would mention the speed and color of the water, the size of the stream, and perhaps the landforms around the stream. Hydrologists, scientists who study water, do much the same thing when they study streams and rivers. They examine a variety of characteristics, including how fast the water flows and the size, slope, and roughness of the stream channel. All of these factors affect how the stream flows and consequently influence the evolution of surrounding landforms.

Stream Gradient

Why do streams flow, anyway? The answer to that question seems rather obvious—water flows downhill. Therefore, streams simply carry water from higher elevations to lower elevations. The slope of a stream (known as the stream gradient) is the change in elevation of the stream over a horizontal distance. As you might expect, the highest gradients are found in steep-sided mountain stream valleys that may drop 40 to 60 meters for every kilometer (210 to 320 feet per mile) of stream length. The gradient would be 40 to 60 meters per 1,000 meters or, expressed as a percentage, 4 to 6 percent.

Where would you find the highest gradients for most streams—at the beginning (headwaters) or end (mouth) of the stream? The stream gradient gradually decreases along the length of a stream, from the headwaters (where it is steepest) to the mouth (Figure 11.10). Streams approaching the river mouth may decrease in elevation by as little as a few centimeters over 1 kilometer (gradients of about 0.001 percent). The Nile River in Egypt has a gradient of about 8 centimeters per kilometer (5 inches per mile), and the last 1,000 kilometers of the Amazon River in Brazil drops just 1 centimeter per kilometer (less than half an inch per mile). So, how does the gradient relate to the stream velocity?

Figure 11.10
Variations in stream gradient. Maximum gradient occurs in mountainous areas located near the source; minimum gradient occurs at the stream's mouth.
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Stream Velocity

Anybody who has ever gone whitewater rafting will tell you that much of the fun comes from being hurled from side to side as the raft bounces its way through the rapids of a mountain stream (Figure 11.11). That experience gives the impression that the raft, and hence all of the water in the stream, is moving fast. In contrast, if we walk or drive alongside rivers with low gradients, they appear to be moving relatively slowly—hence the phrase “lazy river.”

Figure 11.11
White-water rafting. A raft passes through Dark Canyon Rapids in Cataract Canyon of the Colorado River.

When we analyze the average velocity of water moving through a stream (the flow), it turns out that our senses are somewhat deceiving us. The average flow of water in the high-gradient part of a stream is typically slower than that through the low-gradient part of the stream. How can that be so? What makes a high-gradient stream different from a low-gradient stream? Look closely at Figure 11.11. How might the features you see there compare to what you would observe in a low-gradient river? The banks along the steep mountain streams typically have rocky channels. As one continues downstream, the streambed composition changes from gravel, to sand, and eventually to fine-grained silt and mud. This characteristic of the stream channel is called the channel roughness.

How do you think the presence of boulders would affect the flow of the stream? Think of the water as going through a maze. The boulders cause the water to become turbulent (chaotic). It goes forward, then sideways, and sometimes even backward before it moves forward again. Compare that to the flow through the downstream portion of the river where the channel is smooth. Flow there is streamlined (laminar) because there are few obstacles in the channel to disrupt the flow. The channel roughness found in a high-gradient stream actually reduces the average stream velocity when compared a low-gradient stream.

But wait, there's more—a third characteristic, cross-sectional area, is involved in determining stream velocity. Cross-sectional area is determined by multiplying the stream's width by its depth, assuming a rectangular channel shape. (We are simplifying here. Most channels have more complex shapes that are carefully measured to determine cross-sectional area.) Consider cutting a slice through the cross section of a stream as represented in Figure 11.12. The bed and banks of the stream channel exert frictional drag on the passing water. The actual amount of drag is proportional to the length of the surface of the channel banks and bed in contact with the water (that distance is called the wetted perimeter). In streams with the same volume of water and same channel roughness, the channel with the larger wetted perimeter exerts more frictional drag on the water and so has a lower stream velocity (Figure 11.12b). Generally, the larger the stream discharge, the less significant the effect of frictional drag from the wetted perimeter.

 
Figure 11.12
Determining stream channel characterisctics. a. Cross-sectional area (xs) and wetted perimeter (wp) calculations for a rectangular stream channel. b. Three channels with the same cross-sectional area (360 square meters) but different lengths of wetted perimeters. If all other factors were equal, velocity would be highest for Stream C.

The combined effects of these factors (gradient, channel roughness, and wetted perimeter) generally determine the average velocity of a stream. In simple cases, the steeper the gradient, the smoother the channel, and the shorter the wetted perimeter, the faster the velocity. However, these parameters often offset each other. For example, high-gradient streams often have more channel roughness, while the smooth banks and bed of low-gradient streams exert less friction on the flowing water.

At its source, the Mississippi River has a cross-sectional area of 10 square meters (99 square feet). In contrast, closer to its mouth, it has a cross-sectional area of 2,500 square meters (26,240 square feet). The velocity of the Mississippi River at its source is 0.5 m/s (1 mph), while it cranks along at a merry 1.3 m/s (3 mph) as it passes New Orleans on its way into the Gulf of Mexico. Typically, cross-sectional areas of streams increase downstream as more and more water is added to the stream through tributaries. At the same time, channel roughness tends to decrease because particles on the stream bed are smaller. Thus, water in a stream moves faster as it moves downstream.

Checkpoint 11.9

Explain why stream velocity would change along the same section of a stream at different times of the year.

Stream Discharge

In addition to cross-sectional area, just described, there are other ways of assessing a stream's size. In terms of length, the Nile River (6,825 kilometers; 4,240 miles) beats out the Amazon (6,450 kilometers; 4,008 mi) and Mississippi rivers (6,260 kilometers; 3,890 miles). However, we can also measure the volume of water that flows out through the stream. Stream discharge is the volume (cubic meters or cubic feet) of water that passes a given point in one second. The discharge is calculated by multiplying the cross-sectional area by the velocity of the stream flow (Figure 11.13).

Figure 11.13
Stream discharge. Discharge is a measure of the volume of water that passes a point in a given time and can be calculated by multiplying the area of the stream channel (width × depth) by the distance traveled in a given time (velocity).
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Checkpoint 11.10

A stream channel narrows between support columns under a bridge. If discharge does not change, predict how stream velocity would be altered as water flowed under the bridge.

  1. Velocity would increase

  2. Velocity would decrease

  3. Velocity would not change.

Answers

Checkpoint 11.11

Some scientists predict that global warming will result in a corresponding increase in evaporation from the oceans. How would this affect the discharge of the Amazon River?

  1. Discharge would increase.

  2. Discharge would decrease.

  3. Discharge would stay the same.

Answers

Imagine placing an empty 1-gallon milk jug in your kitchen sink. Adjust the flow of the faucet so that it takes 1 minute to fill the jug with water. The volume of water that flows out of the faucet in a minute is the discharge. If the gallon container fills in 60 seconds, the discharge from your faucet is 1 gallon per minute. Now repeat the experiment but reduce the discharge from the faucet so that it takes 22 minutes to fill the gallon jug. You have just modeled the difference between stream discharge in the Amazon and Nile rivers. (For comparison, it would take about 10 minutes to fill the jug using the Mississippi River equivalent.)

Discharge from the Amazon River is about 200,000 cubic meters per second (7 million cubic feet per second) and accounts for 20 percent of all freshwater discharge from streams on Earth. To put it another way, 50 million gallons of water discharge into the Atlantic Ocean from the Amazon River every second! We will discuss how measurements of stream discharge become critical in tracking the potential for flooding in Section 11.6. But first, we will examine the impact of changes in stream velocity and discharge on a stream system.

Checkpoint 11.12

Create a concept map that illustrates the connections among the factors that influence stream flow. Include the following eight terms and up to four more of your own choosing.

discharge velocity wetted perimeter
depth gradient channel roughness
cross-sectional area width