And how much water is needed?

It's not the unit volume cost, it's the total cost.

The United States consumes about 20 million barrels of oil per day. That's about 840 million gallons.

Water consumption is 322 billion gallons/day, 380 times more. That's about a thousand gallons per person per day.

Note that this isn't individual direct consumption (drinking, cleaning, bathing), but the net total use. If you're looking at replacing all city consumption (residential, commercial, industrial) plus agrigulture, you'd be moving these volumes of water. Even at pennies per gallon, the costs add up.

Keep in mind that the watershed for major Western US cities already extends over hundreds to thousands of miles. A chief reason that the Western US looks far more like an island archipelligo than the richly-settled East is because of water scarcity and prior claims.

https://upload.wikimedia.org/wikipedia/en/4/48/Earthlights_d...

San Francisco (and much of the Penninsula) draws water from the Hetch Hetchy Reservoir, 180 miles east. Los Angeles draws much of its water from the California Aqueduct, streching over 500 miles north, and the Colorado River, whose watershed extends to the eastern front of the Rocky Mountains, 1,500 miles to the east. Both delivery systems operate virtually entirely under gravity flow.

The California aqueduct has exceptions --- there are pumping stations in the Delta which provide a few metres of lift, and the Edmunston Pumping Plant which lifts water over the Tehachapi mountains utilises 14 * 80,000 horsepower pumps (835 combined MW) to provide 600m (1,926 feet) of lift to 2 million gallons/minute (7.5 million litres/minute), 7,500 tonnes of water per minute --- roughly the capacity of the Oroville Dam spillway at peak capacity, for comparison. It has its own dedicated 1 GW capacity generating plant.

Note that when the Oroville reservoir is discharging water it is generating electricity. What you gain in shipping Oroville water you lose shipping Tehachapi water. The opportunity cost is not 835 MW, but 1,670 MW. At retail California rates, that's nearly $200,000 per hour of operation, $4.6 million per day, $1.7 billion/year, to move water 750 km across land and 600 m high ... and that's only considering the Edmunston plant itself (there are numerous other pump stations in the system as a whole).

The California Department of Water Resources annual budget is about a billon dollars (there's considerable variation).

So long as you want to use / access water where it's flowing already, costs are low. Major river systems (the Mississippi-Missouri-Ohio-Red river system in the US is among the largest in the world) provide just that.

But when you start wanting to move water laterally, or worse, through or over mountains, costs increase tremendously.

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References:

US petroleum use: https://www.eia.gov/todayinenergy/detail.php?id=44556

US water use: https://www.usgs.gov/mission-areas/water-resources/science/w...

Edmunston Plant: https://en.wikipedia.org/wiki/Edmonston_Pumping_Plant

Oroville Dam: https://en.wikipedia.org/wiki/Oroville_Dam_crisis

California Aqueduct: https://en.wikipedia.org/wiki/California_Aqueduct

CA DWR budget:
https://lao.ca.gov/Publications/Report/4103