In Pathfinder this magical item was recently purchased by our party member. It says that it can put out of 5 gallons of water per second from a 1ft diameter circle. How would you go about calculating the force the water would put out? Specifically, would this be able to propel a rowboat?

Additionally, would using a nozzle help, and if so, could you attach one to the decanter's flow?

Looking for RAW, we could always ask our GM to make a snap decision about how this works, but we're curious about the limitations of physics, given that most of this is measurable

  • \$\begingroup\$ It's not clear if you want a mechanical RAW answer or an intuitive realistic answer. Could you edit your question to specify which? \$\endgroup\$ – Axoren Jul 25 '18 at 4:05
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    \$\begingroup\$ What Erin said ^. \$\endgroup\$ – korkor34 Jul 25 '18 at 4:12
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    \$\begingroup\$ @korkor34 Your comment and your edit don't match up. By RAW, the item does not propel boats because it doesn't say it does. It simply produces water and has a chance to knock the holder of the decanter down in place. It seems like you're somewhere in between. \$\endgroup\$ – Axoren Jul 25 '18 at 4:21
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    \$\begingroup\$ @Axoren If it exerts force on its holder, then it can propel a boat. That's how exerting forces works. It doesn't need to spell out all possible consequences of its described effects. \$\endgroup\$ – Mark Wells Jul 25 '18 at 5:33
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    \$\begingroup\$ I'm voting to close this question as off-topic because it’s purely a real physics question. \$\endgroup\$ – SevenSidedDie Jul 25 '18 at 5:44

Pathfinder's Decanter of Endless Water is a sad shadow of its former D&D glory.

The description isn't internally consistent unless you assume "spray" means that the water is mixed with air (or some other substance), and water streams are not usefully measured by length. But let's make some assumptions and see what we can do:

The decanter spits out a stream "20 feet long." For simplicity, pretend that's straight up in the air, which will give us the most force here. That says the initial velocity is reduced to 0 after subjected to a 32ft/sec deceleration, so d=(1/2)at^2 = 20 = 16 t^2, t is about 1.1, so this decanter is sputtering out about 36 feet per second, or 11 meters/second.

It's throwing 20 gallons of water per round at that speed, which is 3.3 gallons/second. A gallon is 8.3 pounds, so that's 27ish pounds, or 12 kg/second.

Put together, that's 132kgm/s^2, aka 132 Newtons of force. 1 Newton is roughly 1/4 pound, so its roughly 33 pounds of force from the water.

There's a little more, but it probably doesn;t change anything. 33 feet/second in a 1 foot diameter is about 26 cubic feet of stuff per second. The water occupies less than 1/2 cubic foot (the inconsistency mentioned earlier), so only about 2% of what the decanter sprays is water. What else might make up that stream is completely undefined. If it's air, it adds about 10% more force. If it's something else, the answer is even less well defined.

  • \$\begingroup\$ excellent contribution, I expect this is exactly what they were looking for! \$\endgroup\$ – Erin B Jul 25 '18 at 12:33

Using a paddle boat, or functionally a water wheel, you could always drop the water, 8.34 pounds(1 gal of water) * 5 is 41.7 pounds per second.

This might be a non-trivial amount of force to get a boat moving on calm water, depending on the load.

Alternatively, a table in this source suggests that with a 12" diameter pipe, the velocity would be 0.85 ft/sec given the flow is 300 gallons per minute.

  • \$\begingroup\$ Depends how far you drop it, unfortunately. \$\endgroup\$ – fectin Jul 25 '18 at 5:08
  • \$\begingroup\$ @fectin, I think that we can assume the terminal velocity for the water. After a certain point, distance doesn't matter. In my universe, terminal velocity is the speed at which the water dies. \$\endgroup\$ – ShadoCat Jul 25 '18 at 18:19

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