When I set up this experiment, I expected to determine whether pressure is transmitted instantly or a couple tiles per tick. It didn't quite work like either of those ways.
First, the river didn't flood at all until the entire thing was 7/7 and there was a 7/7 tile of water above it.
First I tried starting a flood without closing the output on the pump device. The output tile filled up to 7/7 and there were plenty of paths of 7/7 water to the edge of the river and to the source end (east side of the map), but it would not flood. I waited quite a while, as you can see in the movie. Eventually I decided it wasn't working, and pulled the lever to close the output hatch.
Once the river was almost completely refilled, I ordered the lever pulled to open the hatch. As you can see here, by the time a dwarf pulled it, the river was completely 7/7 (except the tiles to the west blocked by floodgates).
It was several more seconds before anything happened. But what happened next was quite remarkable.
The river did not overflow its bounds all along the map, so the overpressure was not transmitted instantly. However, neither did a pressure wave fly out to cause the river to begin overflowing gradually. Instead, an overflow started centered on the pump tile and spread out in a circle from there.
I immediately ordered the river source (east) floodgates closed, but closing them had *no effect* on the flood! It continued spreading rapidly - as if the pump itself, or the output tile, had become an infinite water source. It even managed to get into the underground parts of the fort, and flood them completely before anyone could stop it.
In the final analysis, we created a small lake's worth of water without any water source to power it.
(Note: The river on this map normally flowed in from the east, and drained to the west. No water ever entered the map from the west - I only built the floodgates to the west for this experiment in particular.)
Save file: http://shadowlord13.googlepages.com/waterPressureInRiverExperiment.7z
By the way, some times of interesting things in the movie:
0:56: River is 7/7 and hatch at pump's output is opened. Conditions for flood exist.
1:00: Flood begins. I pause the game immediately to examine things and order the east river-entering-map floodgates closed.
2:06: The underground fortress's flooding starts
2:34: Water gets into the lower grassy underground level.
2:36: Water flows up out of the lower level and into the more grassy level above it.
2:42: Unpause after ordering a wall built.
2:44: Pause to order a door built because the water is clearly going to hit the wall before anyone gets near enough to build it.
2:48: Water reaches the wall.
2:49: Water fills the area behind the wall, and is now flowing down a 1-wide corridor.
Also 2:49: Water begins moving 3 tiles per tick in the 1-wide hallway (judging by how fast the 7/7 water progressed).
Also 2:49: Water passes the door, and runs over some stairs down to another level.
Also 2:49: Water passes the dwarf carrying the wall's rock.
2:50: Water reaches stairs into the fort.
2:54: Pause to examine how much of the fort has been flooded.
3:09: Entire fort flooded. By this point, everywhere else floodable on the map has already been flooded as well. (Though the swimming training room escaped being completely flooded - only a layer of 1/7 with a bit of 2/7 water managed to get in there)