You can do that, but the cost of building them would be very high. If you what to divert water from a flood you need pipes that have a size larger than natural rivers’ other waterways, they clearly do not have enough capacity to do it.
The amount of water that is missing in a drought is enormous. Look at for example Califonia where the dryest year had 9.4 inches of rain and the wettest 41.66 inches. The average is 22.9 inches. So the dryest year was 13.5 inches = 0.3429 meters less than the average
The area is of the state is 423,970 km2 so the missing water volume was 423970*0.3429*10^-3 = 145 cubic kilometers of water= 145 billion cubic meter= 38 trillion gallons
The average disagree of the Mississippi River is 16,800 cubic meters per second. So we need the average water flow in 8.6 million seconds = 99 days. So the missing amount of water is 27% of the water that flows through the Mississippi.
When you use them unless there is a drop in elevation you need to use a pump to move the water up in elevation. That is like running a hydroelectric power plant in reverse. It is done as a way to store energy in [https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity](https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity)
So there is a land with higher elevation in between you need tunnels. If the endpoint is higher up you need to pump up water.
For droughts this ignores the problem that there likely is not enough excess water available in other locations, you would need enormous dams to store water where extra is available to have enough to fix a drought.
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