Stream Discharge Multiple choice
Floods and Flooding

Stream Discharge

The Mississippi River lapped at the City of Keokuk on July 7, 1993, as it flooded the municipal water pollution control plant in the foreground(U.S.G.S.).

The discharge of a stream is the product of its velocity (V - length of travel per unit of time such as feet/second) times depth of the water (D - unit of length) times width (W of the water - units of length). (Make sure all all three lengths are expressed in the same unit.)

Discharge = V x D x W

If length is measured in feet and time in seconds, Discharge has units of feet3/sec or cubic feet per second (cfs).

Depth times Width gives the cross-sectional area. The shape of the channel is important because of the reduction in velocity due to friction along the channel margins. In a natural situation, an increase in discharge (cubic feet/second) will result in an increase in all three parameters - the river becomes wider, deeper and flows at a higher velocity.

When a stream channel can no longer accommodate increased discharge it overflows its banks and a flood occurs.

For a given drainage system, there will be a maximum depth of water that the channel can hold without overflowing its banks. Stream stage (or water level) and streamflow (or discharge) are measured at locations called streamflow gaging stations. Stage is measured and recorded continuously by electronic instruments.

When flooding is likely to occur the media usually provides the current level (stage) of the water in the channel and the level that must be exceeded for the water to leave the channel and begin to cover the flood plain.

Flow (discharge) is more difficult to measure accurately and continuously than is stage. Discharge for a gaging station is typically determined from an established stage-discharge relation, or rating curve (U.S.G.S.). That is, the hydrologists familiar with the history of a particular drainage basin can accurately predict discharge by measuring stream height (stage).

A stream has a width of 20 feet and a depth of 5 feet. Its cross-sectional area is

100
100 feet
100 feet squared

The velocity of this stream is 10 feet per second. The discharge of the stream is

1000
1000 square feet per second
1000 cubic feet per second

Engineers fix the stream so that its width and depth cannot increase. Perhaps they force the stream to flow through a concrete liner. A flood occurs and the discharge increases to 10,000 cubic feet per second. What is the velocity of the stream?

100 feet per second
1000 feet per second
10,000 feet per second

The velocity of a stream usually increases downstream. The gradient (slope) of the stream typically decreases but gravity, elimination of bed roughness and an increase in the amount of water from the entry of tributaries tends to increase the velocity.

Similarly, the increase in the amount of water and the typical increase in width and depth of the stream allow the discharge to increase downstream.

The United States Geological Survey maintains the United States NWIS-W Data Retrieval web page. You may use this resource to download data from one of several thousand gaging stations. In the next section more informtion will be given as to how to use this resource.

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