very basic fluid statics and dynamics question

consider the image on the drawing at the top (above the yellow arrow)



if i had some non-compressible fluid enclosed in a pipe like container that looped back in on itself (as shown in figure), and if the container was non-elastic, when i rotate this container filled with fluid such that the long axis is vertical, i suspect, that for a short lived time interval, that there will initially be greater pressure at the bottom (where the red arrows are), and there will be a negative pressure at the very top (green arrow). However, because the fluid is incompressible, and encased in a closed container (there is no air inside the container), i suspect that any pressure gradients in the fluid will quickly equilibrate with the rest of the system (fluid). so, my question is, when i rotate the container such that its long axis is vertical, will i get an increase in pressure in my system? or will the pressure gradients cancel exactly?