If you do want to emulate inductance in a water analogy it would be a pump connected to a flywheel.
The pressure (voltage) pushes a flow (current) trough the pump making it work in reverse as a hydraulic motor to spin up the flywheel, then after the pressure is removed the flywheel keeps turning the pump that keeps pushing a flow trough the circuit. The bigger the inductance the bigger the flywheel.
If you then want to turn this into a coupled inductance (for example for building a power transformer) then you would link two of these pump-flywheel assemblies with a common shaft. This way pushing current trough one 'inductor' also spins up the flywheel of the other inductor to drive the pump and produce a flow on the other side. Tho this has the problem of also working with "DC flow" as the assembly will just keep spinning with a steady flow. A more accurate acting example would be to replace the positive displacement style pump with a dynamic type pump (such as a axial flow pump, these pumps produce RPM dependent pressure rather than flow) and replace the flywheel with a rubber band. That way the pump can only turn so many times before the rubber band is making as much torque as the pump can produce at such a flow rate (DC steady stage in an inductor). Then once the flow is removed the rubber band can overpower the pump and start driving it backwards, producing a "back EMF" in that inductor as well as the coupled inductor. In this case the rubber band tension is the magnetic field that can only get so large at a given current, once collapsing returning its stored energy.
At this point water based analogies of electricity start to go a bit too far. But they might help someone picture how an inductor works.
For example the so called "Ram Pump" is an excellent example of a switchmode boost converter done using only water (it pumps water up hill using no external power source):
https://www.permaculturenews.org/2014/04/02/ram-pumps/It uses the momentum of the water flowing down a pipe as an inductor. Letting the water flow out the end to let it build momentum before suddenly shutting the end off to make the water hammer itself into the value, producing lots of pressure, that then gets rectified by a check valve (a diode basically) to a steady high pressure that is used to push water up a hill.