Let say when the pistons are kept stationary the height of the water columns are h. And we start exerting extra force on the left piston in figure, and the pistons are moving with constant speeds. Since velocity of water increases when it enters the narrower part, that means there is an acceleration. Hence there must be pressure difference from wide part to narrow part where the shape of the pipe changes. So the pressure in the wide pipe is bigger than the pressure in the narrow part.
My questions: 1) can we also say that both of these pressures are lower than the pressure there before we start moving the pistons? That is to say new column heights are both lower than h.
2) the same question but this time we start pushing on the right piston with constant speed.
Note: When I say pressure, I mean the pressure exerted by the fluid on the upper part of the pipe.