Ink flow is primarily due to gravity flow.
Bulk ink/cartridges are at approximately the same level as the head.
The ValueJet 64s and 100s, have a sub-tank system at the level of
the head, but the cartridges are located above the head. Valves
control flow into the subtanks, allowing for ink cartridge changes
without interrupting printing.
A pump actually pulls ink through the head during filling and
cleaning cycles by creating a vacuum between the bottom of the head and
the capping station seal. Failure to keep the bottom of the head clean
and the seal clean and in good condition will limit the ability to pull
ink through the head. This may result in nozzles NOT being cleaned
properly and will affect the volume of ink
values being writting to the smart cards on carded cartridges.
The smart cart counts the number of pump cycles (and number of nozzle firings) to
estimate the amount of ink used. It writes
this information to the smart cart to record the amount of ink remaining in the cartridge.

Thanks to Allan at:
http://www.ajh-designs.com/
for the graphic.
The Ink Status is most often assumed to be the amount of ink in the cartridge but in one case it is not correct.
The main issue is with the first cartridge when an INK FILL is performed.
You
are correct in that ink volume is subtracted for every cleaning
function or printing operation. The exception is that the INK FILL
process uses 50% of the cartridge (on a 220ml) just to fill the sub
tank. Yet if you immediately read the INK STATUS menu it will still
show 87% (48), 82% (64) and 77% (100). For the remainder of the
original cartridge (after any INK FILL) the customer must subtract 50%
to know how much ink is in the cartridge. Once the original is changed
out then the new cartridge will read 100% and again start counting
accurately or at least to the degree that the seal is working
properly. With a second ink cartridge the INK STATUS will correctly
display how much ink is in the cartridge.
The
subtanks in the VJ16xx and VJ26xx series allow for cartidge changes
without interrupting printing, the 1204 and 1304 series will stop
printing when a cartridge is removed or when the 'empty' tab protrudes
enough to activate the empty sensor. There are reports from customers:
"I heard the beeping but I was told to keep printing until the printer
stops printing and then replace the cartridge." Of course, this
is poor advice and not the way the printer is designed. What can be
confusing is the 'beeping' - it really means FEED ME NOW, not wait
until I stop printing.
KEY
POINT: The INK LOW tab comes out when ink is flowing from the
cartridge into the sub tank. Ink flows into the sub tank when the
solenoid valve is open. The valve opens when the 'low ink sensor' in
the sub tank opens. So the low subtank wants to FILL and it sends the
signal to open the solenoid. Once the solenoid opens, ink flows by
gravity into the sub tank until the sub tank HIGH sensor closes.
However, if the INK LOW tab of the cartridge pops out during the
gravity feeding then the printer begins 'beeping' and should close the
valve. When the low amount of ink in the sub tank is consumed then the
printer will stop printing with an 'Ink End' message.
We
also discussed that if the counter drops to a low point the printer
will display 'ink near end x' and may start beeping as well. This
would occur when the pump/cap are not pulling the full amount of liquid
during the 'cleaning' cycles.