Hoppy, you're pretty close, but I've got a couple of issues with your original post. The pump in a typical canister is located after the media and before the return pipe. The pump imparts added pressure, so the pressure on the outlet side is 36" + delta P, making it very easy for the pump to push water up the return pipe. It will actually be able to raise a water column to somewhere between 2' and 10' above the aquarium surface level depending on the specific pump. There is no siphon effect on the outlet side. A siphon implies negative pressure. Powerheads manage very little head because their pump vanes are designed to operate in near-zero head conditions.
In actual practice, the head at the inlet side of the pump will be something less than 36" because the situation is not static. There is head loss at the inlet strainer, along the inlet tubing, at fittings, and through the filter media. The effect of same-diameter fittings is minor. By far, most of the energy lost in the system is due to high-velocity flow along a long section of relatively narrow tubing. The velocity of flow in the media portion of the canister is very small, since the diameter is enormous, even when the media is fairly dirty.
It is possible to develop a negative pressure situation if the inlet tubing is too narrow, if it is too long, or if the pump isn't located at least a little bit lower than the aquarium. Eheim inlet tubing sizes are usually larger than outlet sizes to ensure that a negative situation (with resultant cavitation & noise) doesn't develop.
Thought experiment: A canister filter placed 100' below an aquarium will have very low output compared to one placed 3' below the aquarium, but it's only because of the energy lost along 200' of tubing. For comparison, a canister filter located 100' below the aquarium that is serviced by 6" diameter inlet and return pipes (almost zero flow velocity) will develop more flow than one 3' below the tank using typical 1/2" tubes.
Next thought experiment:
The loss of head (pressure) in a horizontal pipe due to friction (turbulence) is expressed by the Darcy-Weisbach equation:
f is a coefficient that comes from a Moody diagram (which accounts for laminar vs turbulent flow)
L is length of the pipe
V is the velocity of flow
D is inner diameter of the pipe
g is the gravitational constant (32.2 feet per second squared)
For our purposes, assume
f is constant. Within reasonable limits, this is an ok approximation.
Assume a 1" inner pipe diameter, a 10 foot section of pipe, 500 gallons per hour flow, and an f of 0.03 (a typical value).
Velocity in this setting is 4.7 feet per second and total head loss is 1.25 feet.
Change the pipe to 3/4" diameter and velocity becomes 8.4 fps with a head loss of 5.3 feet.
Just for fun, assume 200' of 6" diameter pipe. Velocity is 0.13 fps and headloss is 0.0032 feet.
Lets go back to our initial values of 10' of pipe (typical) and 1" tubing (generous). Now, lets use 9.8 feet of 1" pipe and 0.2 feet of 1/2" pipe to simulate the fittings. If there is a smooth transition zone into and away from the fittings (to minimize turbulence), this is a reasonable assumption.
Head loss from 9.8 feet of 1" pipe is 1.23 feet.
Head loss from 0.2 feet of 1/2" pipe is 0.80 feet.
The energy loss in a 0.2 foot length of 1/2" diameter tubing is almost as large as the energy lost along 9.8 feet of 1" pipe!
In real life, when you turn the power on, the flow through a canister filter will increase from zero to a value where the pressure (energy) lost from turbulence (friction) equals the pressure (energy) added from the pump. As flow rates increase, pumps have less ability to impart energy (see a pump curve). At zero flow (shutoff head) pumps will produce the most pressure.
As flow picks up, velocity in the pipes also increases. The added velocity produces friction which robs energy from the system (headloss). Once the sum of headloss from each section (pipe, fittings, media compartment) equals the head added from the pump, a static condition is reached. There are a lot of moving targets here. Water acts funny when it transitions from laminar to turbulent flow. Centrifugal pump curves aren't straight lines (despite what Eheim publishes).
Fascinating stuff, fluid mechanics. Pump designers are smart dudes!