RUNOFF – FLOWING WATER

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Four things to consider about water in a stream:

1. How does the water get into the stream?

2. What are the ways that the water can move internally as it proceeds downstream?

3. How do we characterize how much water moves through the stream?

4. What factors affect the velocity (or the speed) of the stream water as if flows?

1. How does the water get into the stream? Sheetwash and Tributaries

Imagine a rain of consistent intensity across the side of a hill. Further, suppose that the ground is already saturated, so all the water runs off. At the top meter of the hill (m1) the runoff will be equal to the amount of water falling on that meter of hillside – call it one unit of water. In the next meter downhill (m2) the water coming in from m1 will be added to the water falling in m2 for a total of 2 units of water. In m3 the combined flow will equal 3 units, and so on. The amount of water moving across the ground will increase down the hillside.

m1 – 1 unit

m2 – 2 units

m3 – 3 units

m4 – 4 units

Only a trickle of water will flow across m1, but across m2 there will be a noticeable sheet of water. However, there will be no pattern to this flow – no channeling, nothing dry – the entire surface will be covered in water. We call this sheetwash or overland flow. Lower, say in m3, the additional water will give the flow a little more erosive power and the stream will begin to excavate small, but noticeable channels for itself called rills. Here the water first begins to be channelized, with some drier places between the rills. Even lower, say by m4, the rills will join into larger channels that will be obvious even after the rain has stopped. Even though there will be no flow in them between rains they will obviously be stream channels. Such channels, only carrying water during and soon after a rain, are called intermittent channels. They can actually be fairly large.

Map view: Top of Hill Lower Part of Hill Base of Hill Farther Downstream (Headwaters)

Sheetwash Rills Intermittent Permanent Tributaries Trunk Stream (or Tributary to Something Bigger)

Water runs willy-nilly downslope

Water collects into larger channels as smaller ones join.

2. What are the ways that the water can move internally as it proceeds downstream?

Laminar and Turbulent Flow

(Small scale characterization of water movement)

TYPES OF FLOW IN A CHANNEL: LAMINAR vs. TURBULENT

The word “velocity” is going to come up frequently as we talk about streams, and unfortunately it can be a little confusing if you don’t keep up with the context in which it is used. A stream’s velocity or average velocity is the rate at which it moves water down its course – how fast it delivers water to its mouth for example. Counter-intuitively, streams tend to have higher average velocities farther downstream, even though the gradient (slope) is lower. They have lower velocities near their heads where it looks like they are rushing along at breakneck pace down the steep slope. Part of the explanation is that the flow of most of the water in the downstream segments is nearly laminar, so it makes more downstream progress in a given amount of time. Upstream, where the gradient is higher, the water is much more turbulent, so even though it is, in some sense, moving faster it is not moving downstream as much. Instead, it eddies, is diverted around obstacles (like big rocks), and tumbles over coarser gravel in its bed. Velocity and speed are not the same thing.

Here’s a good analogy. A couple of times a year there is a NASCAR race at Atlanta Motor Speedway, west of I-75 near McDonough, GA. If a car on the freeway passes the racetrack just as the race starts and drives at a constant speed of 60 mph the driver will arrive at Florida in a little 4 hours (his odometer will show he has gone some 250 miles). Meanwhile, the racers drive at speeds averaging around twice that (120mph) of the person on the freeway. In a little over four hours their odometers will indicate they have gone 500 miles. But they will end up at exactly the same place they started. Their progress in any particular direction is zero miles in four hours. Who went faster? The average velocity of the driver on the interstate was greater because more progress in some direction was made. The moment or instantaneous velocities of the racers was much higher, even though they didn’t make any progress in any particular direction. The next slide illustrates the concept.

RACE DAY! North

Atlanta International Speedway

I-75

Average “speed” of cars in southbound

lane = 60mph

Start/ Finish

Line

Average “speed” of cars on track =

120 mph

Southward progress of any “average” individual car or cluster of cars traveling together for any hour of the

race = 0 miles. “Velocity” = 0 mph!

Southward progress of any “average” individual car or cluster of cars traveling together the same hour =

60 miles. “Velocity” = 60 mph!

At a large scale when we talk about a stream’s velocity we mean the downstream progress of a certain volume of its water in a certain amount of time. At a very small scale (when we talk about the forces that move an individual piece of sediment) we also talk about the velocity of the water, but that usage is a little different. We are interested in how fast the water moves over a grain at the instant it is lifted (or not lifted). We don’t much care if the water is moving directly downstream or not. Overall average velocity of a stream doesn’t say anything about local moment velocity affecting sediment. Moment velocities of lowland streams at their beds are lower than those of mountain streams, so they cannot move sediment as coarse. The water has a higher downstream velocity, but it isn’t moving as fast where it counts! For a variety of reasons turbulent flow is more effective at moving coarser sediment than laminar flow is. Even though a stream has a higher velocity downstream, the size of its bedload always decreases downstream!

3. How do we characterize how much

water moves through the stream? Discharge

(Large scale characterization of water movement)

“Discharge” means the total amount of water moving through a stream. It is mathematically expressed as a volume of water passing a point per unit of time. Usually we use m3 (cubic meters) per second, but feet3/second or gallons per day are also commonly used, particularly when the intent is to emphasize just how much water is actually flowing through a large stream. We can determine a stream’s discharge with a few simple measurements of the channel (with a meter ruler or tape) and the velocity (with a current meter or a float). We need to know the channel’s average width (w), so we use a tape or other device to measure that (in meters) at various depths (say every meter) then average those values. We also need the average depth (d) and so measure that across the stream, perhaps, again, at every meter. Then we average those values. These two averages multiplied together give the cross-sectional area (A) in m2. We also need to know the average velocity. Since this is lower at the bed and banks than in the top center we ideally use a current meter and measure on a grid. If we don’t have a current meter we can still estimate the velocity by timing a float moving downstream in various places – close to the sides, in the middle, etc. We do this many times and take the average. This will not tell us about the velocity at depth.

When we have these three values we simply multiply them together:

Width (in m) x Depth (m) x Velocity (m/s) gives us Discharge (m3/s)

or

w x d x v = Q

(or A x v = Q)

(Q is usually used for discharge rather than big D since little d is “depth”.)

Make sure you see how the units work:

m x m x m/s = m3/s

Average Width = 4m Average Depth = 2m

Float moves an average of 20m in 10 seconds (2 m/s)

Imagine that we have measured a stream and found the width, depth and velocity indicated in the diagram.

What is the discharge?

Q = w x d x v in this case:

Q = 4m x 2m x 2 m/s = 16m3/s

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=100m3/s

PAY CLOSE ATTENTION: This is very important. Unless the total amount of water in a stream changes the discharge will be constant throughout its course. We are about to explore how the flow of a stream changes under various conditions and there will probably be test questions about this material. Unless the question indicates that water is added or lost, “the discharge changes“ is NEVER the answer! NEVER! I say this because, judging from past experience, whatever I do roughly a third of you will miss these questions because you will insist on having a stream’s discharge change. It doesn’t seem to matter how emphatically I say that the discharge cannot change. Any amount of water that flows into one stretch of a stream must also flow through every other downstream stretch. It cannot go away for a few meters or kilometers and then come back for others. It must flow through every meter of the stream. In this example 100m3/s flows in at the left end and 100m3/s flows out at the right end. At every point along the stream the discharge is 100m3/s.

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=150m3/s

Q=150m3/s

Q=150m3/s

Q=50m3/s

Q=50m3/s

Q=50m3/s

One way to increase discharge of a stream is to add water to it through a tributary. In the example a tributary stream with Q=50m3/s joins a stream with Q=100m3/s. The resulting trunk stream has a discharge beyond the confluence of exactly the sum of the two – 150 m3/s.

Here are the ways – all the ways – that discharge can change.

Q=100m3/s

Q=110m3/s

Q=120m3/s

Q=120m3/s

Q=120m3/s

Q=120m3/s

Rainfall also adds water to a stream by both falling into the stream and sheetwash/tributaries from the sides. The discharge at the upstream end of a rain shower will go up by the amount of water added by the rain. At the downstream end of the shower Q goes up by that amount plus the additional water coming from upstream. Beyond the limits of the rain shower the discharge is constant.

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=100m3/s

Q=80m3/s

Q=80m3/s

Q=80m3/s

Q=80m3/s

Q=80m3/s

Q=80m3/s

Conversely, during drought the amount of water normally added to the stream by precipitation and springs is cut, and the stream gradually loses discharge as its store of water flows out the downstream end. Notice that the discharge is

still constant along its length.

Stream at beginning of

drought

Same stream during drought

Q=100m3/s

Q=110m3/s

Q=120m3/s

Q=130m3/s

Q=140m3/s

Q=150m3/s

Q=100m3/s

Q=95m3/s

Q=90m3/s

Q=85m3/s

Q=80m3/s

Q=75m3/s

Recall that some streams (like the Suwannee River) are gaining streams. In these, discharge goes up along the course as springs add water. Incidentally, during periods of low flow most

streams become gaining streams. That is why they do not run dry even after prolonged drought.

Losing streams (like the Colorado River) will see decreasing discharge along their course as water is lost to evaporation and to infiltration.

So the discharge of a stream changes, if and only if water is added to or

removed from that stream.

4. What factors affect the velocity (or the speed) of the stream water as if flows?

1) Discharge We should make an observation here about discharge and its relationship to velocity. In addition to a greater degree of laminar flow most streams have higher discharge closer to their mouths. As discharge goes up, average velocity also goes up. Remember that this doesn’t mean the stream can pick up bigger sediment particles, just that the water is making more downstream progress. Imagine two streams. One is 1m deep and 2m wide and flows at 2m/s (faster). The other is 4m wide and 8m deep, but only flows at 1m/s (slower).

Q for the first stream is 1m x 2m x 2m/s = 4m3/s. For the second it is 4m x 8m x 1m/s = 32m3/s.

Even though the second stream moves only half as fast, it carries 8 times as much water. It would, in other words, fill an empty lake 8 times faster, and so in some sense delivers water faster, even though it flows more slowly. It would also deliver sediment faster, though the sediment would be finer-grained. Moment velocity dictates grain size that can be lifted; discharge (and the average velocity attached to it) dictates volume of sediment carried.

Given that the discharge of a stream is constant along some stretch of that stream (absent water addition) the characteristics of the channel shape can

have a pronounced effect on the flow velocity.

Let’s look at the discharge equation of this hypothetical stream again:

Average Width = 4m Average Depth = 2m

Float moves an average of 20m in 10 seconds (2 m/s)

Q = w x d x v in this case:

Q = 4m x 2m x 2 m/s = 16m3/s

Q = 4m x 2m x 2 m/s = 16m3/s

2) Channel shape

Remember that most that streams flow across surfaces of loose sediment create their own widths and depths to minimize the friction of the water against the bed and banks. Imagine that the stream in the

previous diagram does exactly that in an upper stretch (left), but then flows into an area of solid rock that is more difficult to erode. The rock now controls how wide and deep the stream can erode (though not how high its level can rise. Gravity does that.) Let’s say that the rock constrains the width and depth in this

stretch to ½ what it was upstream.

Discharge (16m3/s) must remain constant. The water that flows into the middle stretch from upstream must flow through at the same rate or else it would pile up to a gravitationally unstable level. Since both w and d decline, in order to keep Q at 16m3/s, v must increase from 2m/s to 8m/s. Here is the reason that

whitewater raft and kayak courses are in gorges!

Q = 4m x 2m x 2 m/s = 16m3/s

Q = 2m x 1m x 8 m/s = 16m3/s

Once out of the gorge (and free again to create its own form) the stream will return to

its stable configuration – 4m wide by 2m deep and flowing at 2 m/s.

1. The Flint River enters the Sprewell Bluff area of Pine Mountain here.

2. All the way through the mountain the river is in a

gorge, and provides a fast and exciting whitewater

ride over numerous rapids, including

Yellowjacket Shoal.

3. It leaves the gorge here and slows back to its original velocity.

4. The coarse sediment it entrained on its fast ride through the gorge cannot be carried farther, and so drops as a series of mid-stream islands here.

The Flint River at Pine Mountain is an excellent example of a stream that does

exactly this.

N

750’

Take Home Message 1. Rainwater moves off slopes adjacent to a stream system and into the stream.

2. Near the tops of the slopes the flow is not obviously channelized, but moves as a sheet of water. This is called sheetwash or (less commonly) overland flow.

3. A little farther downslope the flowing water can be seen to have collected into tiny, subtle channels. However, these rills are not particularly evident when rain is not actively falling.

4. Eventually the water collects into small channels that are always obvious, though only carrying water during and for a short time after a rain. These are intermittent channels.

5. The smallest permanent streams join progressively into larger and larger channels.

6. The largest stream in a drainage basin is the trunk for that basin. We will talk more about drainage basins later.

7. The flow through a channel can be laminar (gentle and linear) or turbulent (rougher and with lots of eddies). Most natural stream flow is more or less turbulent, particularly upstream.

8. Discharge is the amount of water that moves past a point in a unit of time. It is usually expressed in cubic meters per second and measured as width x depth x velocity.

9. Discharge will remain constant through a stream’s course despite changes in the channel shape and flow velocity. The only way discharge changes within a stream is through the addition or water (from rain, springs, or tributaries) or its loss (through evaporation or infiltration to the ground.)

10. If discharge does increase then depth, width, and velocity ordinarily will all increase.

11. The shape of the channel can influence velocity. Very narrow or very shallow channels make for higher velocity.

12. The velocity of a stream is not the same thing as how fast (or, better, how vigorously) the water moves.