Discharge


The analysis of water flowing through stream systems is very important in the study of geology. Moving water possesses energy. This energy, through erosion and deposition, modifies the surface of the earth. Most of the landscape that we see around us is the result of the sculpting of rock by water. The alternating ridges and valleys found in the Appalachians, including the area of Cumberland and, also, Choccolocco Mountain directly east of campus and the valley actually containing J.S.U., were produced by the water-powered differential erosion of folded and faulted rocks. The resulting sediments are carried away in streams, later to be deposited and perhaps transformed into sedimentary rocks. Streams are also important in terms of human activities, being widely used for sources of water, power generation, transportation and recreation. In order to use streams wisely, we must understand their physical characteristics.

Stream Discharge and Stream Geometry

A stream can be generally defined as "a long, narrow body of water flowing in a channel." Streams come in all sizes, from large rivers, like the Coosa, to small artificial streams, such as the gutters on your house.

One very important stream variable is the "discharge." The discharge is the volume of water flowing by a point over a given period of time. For example, a small stream might have a discharge of one cubic meter per second. This means, if you are standing at one point on the stream bank, one cubic meter of water will flow by your position every second.

Discharge can be calculated using the "Continuity Equation":

Q = W * D * V, where,

Q= the discharge (usually cubic meters per second, but can be any volume per time)

W= the width of the channel (usually meters)

D= the depth of the channel (usually meters)

V= the velocity of flow (usually meters per second, but can be any distance per time)

This is an extremely useful equation. If W, D, and V, are known (these are easily measured), then Q can be determined.

1. What is the discharge of a stream that has a velocity of 4 m/sec., a width of 5m, and a depth of 2m? Answer

2. What is the discharge of a stream which has a velocity of 3 ft/sec, a width of 20 ft, and a mean depth of 5 ft? Answer

As a stream flows downhill, the channel geometry (velocity, width, and depth) will change. For example, a stream might become deeper or more shallow, wider or more narrow, speed up or slow down. If we assume that the discharge (Q) remains constant while these other variables are changing, we can rearrange the continuity equation to solve for the new velocity, width, or depth (saving us from having to measure these things again, and getting all wet). Simply put, if you change one variable in the continuity equation, another variable must also change.

For example, consider the stream discussed in question #2, above. You determined that it had a discharge of 300 cubic feet / second. Say that a short distance downstream, this stream narrows to 10 feet and deepens to 6 feet, while the discharge remains the same. In response to these new conditions, the velocity must also change. How?

Take the continuity equation and rearrange it to solve for velocity.

Q = W * D * V

Q / (W * D) = V

Substitute in the variable you know (Q = 300 cubic feet / second ; W = 10 feet and D = 6 feet) and solve for V

300 cubic feet / sec. / (10 ft. * 6 ft.) = V

so,

V = 5 feet / sec.

Solve the following problems.

3. A stream has a discharge of 48 cubic meters per second. It has a velocity of 4 m/sec, and a depth of 2 m. What is its width? Answer

4. The stream in the above question slows to 2m/sec and the depth drops to 1m while the discharge is unchanged. What is the new width of the river? Answer

5. A stream has a discharge of 200 cu ft/sec. Its width is 20 ft and its velocity is 2 ft/sec. A half mile downstream, the stream's discharge has increased to 300 ft/sec and the width has decreased to 15 ft, while velocity remains the same. How else must the geometry of the stream channel change in order to accommodate these downstream modifications?Answer

6. What must happen to the geometry of a stream channel if Q is increased while D and W are not? Thinking about streams in real life, do you think it is impossible to increase this one variable without D and W changing too?Answer

7. What changes will occur in a stream's geometry as it progresses from a quiet, deep stream to a series of white water rapids?Answer
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