I don't think there is any need to wrangle your way through the 'Coriolis' force.
Just look at this simply and imagine what happens to the pumped fluid after it has exited the system. What you are after is for the pumped fluid to have no rotational velocity.
If it has rotational velocity when you don't really want it, then it takes energy to make that happen. This is where your energy is going.
In most air-flow processes, you have static reaction elements that push back against the air so that it exits the flow-modifyer parts with as little rotational inertia as possible. 'Swirl reducers' if you like. You'll find such parts in erverything from vacuum cleaner blowers through to jet engines; static parts that act to cause process air to exit with minimal rotational inertia.