Concept explainers
What happens to stream speed if discharge doubles and the cross-sectional area of the stream channel also doubles?
The change in stream speed if discharge and the cross-sectional area of the stream are doubled.
Answer to Problem 17TE
There will be no change on the stream speed if both the discharge and the cross-sectional area of the stream are doubled.
Explanation of Solution
In a channel, average stream speed is given by discharge divided by cross-sectional area. The discharge is directly proportional to the stream speed. If the area of a stream is constant and the discharge is increased, then the stream speed will increase. And if the discharge is decreased, then the stream speed will also decrease. It will increase or decrease by the same factor with which the discharge is increased or decreased. The area is inversely proportional to the speed. So, if the discharge and cross-sectional area are changed by the same value, the stream speed will not change.
Conclusion:
Therefore, there will be no change on the stream speed if both the discharge and the cross-sectional area of the stream are doubled.
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