The equation of continuity for pipes
$$\frac{\Delta m_{1}}{\Delta t} =\frac{\Delta m_{2}}{\Delta t}$$
states that mass flow rate inside a pipe doesn't depend on pipe diameter. I'm confused on this being valid even in the following scenarios:
In these three different systems, an open tap creates an ideal fluid like magic that keeps filling the larger/taller tank in order to maintain constant pressure.
A pipe depart from each tank at the same level.
Given that the end of the pipes are closed at time zero, and we open them simultaneously when the systems have their tank and pipe completely filled, will the glasses at the end of the pipes fill up all at the same time?
(Assume that the width of each pipe is much smaller than the height of the tank.)
Or in more scientific terms:
Will mass flow rate be the same in these pipes filled with an ideal fluid?