Power of Doubled River
Name: Flitcher D.
Date: March 23, 2004
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
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.
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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