Power recovery turbine?

Could you help me how can we use the dynamics energy of a high speed low pressure (atm) air, exits from a piping system equipped with a fan, without increasing the pressure on the exitting air and accordingly on the fan.

Answer:
You can't. Any such attempt WILL increase the pressure.
You are really reaching for a few crumbs. What makes you think this is a viable energy source?
Any obstruction you place in the flow path will cause back pressure and reduce the dynamic head of the turbine you install and all other turbines in the flow path. You will gain nothing.
With water this might be able to be made to work IF you had a way to restrict the water flow out of the turbine to be less than the flow into the turbine.
Then mount the turbine at the base of a very tall pipe, and let the water build up a deep head within the pipe.
This way you could build up enough pressure on the turbine to drive it.
Open the valve at the outlet of the turbine to allow the water to flow thru it, but make sure that you keep the inflow of water greater than the outflow, so you might need a bypass on the inflow stream to divert the excess water.

Actually, this is how most power turbines work, (i.e. at Hoover Dam). The turbines are located 800 feet below the water level of the dam, and the water flows into and thru an 800 foot high pipe to to the turbines located at the base of the dam. This arrangement maintains a high pressure and a high rate of water flow on the turbine blades.

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