Have a huge debate at work

I'm working as drilling fluid engineer on oil rig (for a purpose of context). I'll will try to describe my question in a simpler examples.

Let's say we have a cylinder 200mm in diameter and 4000m in length (oil well, top is 0 bottom is 4000m). Also we have a 1000m pipe which we lower from top of the cylinder on all of pipes length (90mm inner pipe diameter and 100mm outer pope diameter for example). After that we started pumping, 10 liters per sec (pump flow rate). Liquid that was initially in cylinder and liquid we pumping is the same, non-Newtonian fluid (but I'm not talking about super thick substance. You could imagine oil based lubricants like motor oil). Bottom of the cylinder is sealed. Top of the cylinder is open. So fluid is going from pump to pipe, all the way down to the bottom of the pipe at 1000m and through annular space to the top and then freely spill from the top of the cylinder because of overflowing.

Now the question, how the pressure will distribute from 1000m to 4000m. For example if we have extra 100 atm of pressure from pumping that press at walls of the cylinder at 1000m. What will be left of that extra pressure at 2000m, at 3000m, at 4000m, or because the top of the cylinder is open all the extra pressure will go that way and after some 50-200m extra pressure will be non existent?