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An answer on a related question stated that water injection was used on some of the early jet planes, for example Boeing 707 and Boeing 747-100/200.

I presume the water is stored in some tank. How much water is typically carried for this? And given the water flow rate, what is the usual water injection time available before water runs out?

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This paper here gives a good overview of water injection.

It suggests for injecting water into the compressor, a 300 gallon tank is necessary, for a 2.2% water to core air flow ratio (the historical norm), for injection from take-off to top of climb.

For injecting into the combustor, it suggests a 135 gallon tank, for a 0.5:1 water to fuel ratio, again for injection from take-off to top of climb.

For both of these scenarios, the tank water flow rate was designed to achieve a 50% NOx reduction. The paper gives other water quantities required to acheive different goals (eg different NOx reductions and different turbine temperature reductions).

I don't think the paper indicates how long it takes to get to top-of-climb. I assume these are US gallons, as its a US paper.

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