Water flow calculation

I have a large lake that is 14' vertically above where I want water to be ... he lake is also 350' away from where I want the water.

If I were to lay in a 5" pipe, can anybody calculate the approximate volume of water that would come through the pipe.

I found a resource on line that gives (Assuming Gravity to Low Pressure. at about 6 f/s flow velocity) a single 5? pipe could provide 19,000 gallons of water per hr, a 6? pipe rises to 27,500 galls per Hr.

Any hydraulic engineers here able to advise if this is a good approximation.

Trying to use the lake as a non pumped supply.

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