Total work done in pumping a layer water through a bottleneck

[JustSomeGuy80]

I don't know much about physics but I know that Work = Force x Distance. Does it take more force to pump an x amount of water through a bottleneck (a shrinking radius from a to b and the constant radius from b to c) as opposed to pumping that same amount of water through a constant radius? If so, how do I factor that into the equation?

 

[Gear300]

If the final height of the water is the same, then the same amount of work against gravity should have been done...ideal flow, or laminar flow, disregards collisions against the bottle walls.