What it does not allow though is to limit the flow - one wire can, theoretically, run any current,

You can limit the current with resistance. Make each segment of the pipe have some resistance. This will also limit how far you can transport fluids with pipes and encourage use of trains with fluid wagons.

"Connect" sources (e.g. offshore pumps) to a high potential and assume they have internal resistance. This limits how much current they can output (this is very analogous to an electric battery).

"Connect" sinks (e.g. boilers) to ground (zero potential) and also assign some internal resistance to them. This makes them analogous to an electric load.

This limits the flow through a single pipe to V/(d * r + R1 + R2) where V is the potential the offshore pump is connected to, d is distance, r is the unit resistance of a pipe, R1 is the internal resistance of the offshore pump and R2 is internal resistance of the boiler.

If you only have offshore pumps, pipes and sinks (boilers etc) then your electric network basically consists of resistors. This means that if you write down the Ohm's law for each segment and Kirchhoff's law for every junction, you get a sparse system of linear equations. You could use an open-source solver library to crack that very efficiently. You can optimize it significantly by joining multiple pipe units into segments.

The tricky bit is the electric pumps. At a bare minimum, you want them to conduct only in one direction (basically, making them a diode). Unfortunately, this introduces non-linearity into your system: the Ohm's law doesn't work for diodes, and so you can't use a time-proven sparse linear solver anymore. There must be ways around it though.