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Name: Flitcher D.
Status: Other
Age: 40s
Location: N/A
Country: N/A
Date: March 23, 2004


Question:
I seem to recall from my high school days that if yu double the size of a river (such as might happen with flooding) you> increase its power by a factor much greater than twice. What would a> river's strength be if you doubled its size?



Replies:
The increase in power (energy) depends on how you double the size of the river. If you simply doubled the width of the river with flow to match the current height, then you would double the energy.

However, if you flood a river within its current banks, any extra flow by necessity has to be on top of the current flow. So a doubled flow would be the doubled energy plus then energy needed to lift the water the extra foot or yard or several yards above the current height. How much that height differs depends a lot on the shape of the bank, steep narrow banks will tend to raise the water level more. The greater the change in height the greater the difference in energy, for the same additional flow. That is why they try and build hydroelectric plants with as great a difference in height as is possible.

Don Yee


Fletcher,

The force exerted by the water is proportional to the vertical cross-sectional area of the water, so if you had twice as much water, you would have twice as much force.

However, the force is also proportional to the third power of the speed of the water. So, if, because there is more water, the river is running faster than it does when it is at it's normal height, the power is much greater.

For a simple example, let us say that the normal speed is 1 mph and that the flood speed is 2 mph. Taking 1 mph cubed is 1, taking 2 mph cubed is 8. So, there is 8 times as much force just from the faster speed of the water. Then you have to multiply that by the increased amount of water.

To take a realistic example, let us say that the normal speed of the river is 10 mph and that the flood speed is 20 mph. 10 cubed is 1000, 20 cubed is 8000, again giving eight times the force. Multiply this by twice as much water during a flood and you get a factor of 16 times as much force during the flood condition.

David R. Cook
Atmospheric Research Section
Environmental Research Division
Argonne National Laboratory



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