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Will anybody be able to mention the English word for "Volume per second (or preferably Volume per Time unit) or "Amount of task per a second"?

Thank you.

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    You're asking two distinct questions here. See answers below for variants on 'volume flow rate' (recognising that these are not everyday terms - 'flow rate' would probably be recognised by most men-in-the-street). 'Work rate' is an everyday term for how fast a person / machine is working, but isn't usually described in precise units. 'Power' in its scientific sense is defined in precise terms.
    – Edwin Ashworth
    Commented Sep 10, 2013 at 7:32

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For a general term describing some kind of processing I'd use "throughput"

As Wikipedia states:

Throughput is the movement of inputs and outputs through a production process. [...] Throughput can be best described as the rate at which a system generates its products / services per unit of time.

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There is a French word "Débit" for the volume of fluid which passes through a given surface per unit time.

For English from Wikipedia:

In physics and engineering, in particular fluid dynamics and hydrometry, the volumetric flow rate, (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes through a given surface per unit time. The SI unit is m3·s−1 (cubic meters per second). In US Customary Units and British Imperial Units, volumetric flow rate is often expressed as ft3/s (cubic feet per second). It is usually represented by the symbol Q.

And the French page

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How about the term discharge as used in hydrology?

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