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Since I'm not a physics or math expert, I wanna ask how to calculate the actual force of water launched from a water cannon, and then for example compare it to the forces from a firehose. I know that I did not give any specific data but I assume that I need velocity of water, diameter of hose/nozzle, flow rate and probably something else.

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There is kind of standard trick to solve this problem.

When you apply some force $F$ to a body for a period of time $t$ the momentum of this body will change by $Ft$.

Let's say we have a fire horse which produces a water stream. 1500 liters per minute, speed is $20 \text{m/s}$. (I am not sure these are specifications of some real fire fighting truck).

So, each second 1500 / 60 = 25 liters of water hit the target and stop. Mass of this water is $25 \;\text{kg}$. Speed: $20 \;\text{m/s}$. Change of momentum: $ \text{mass}\times\text{speed} = 500 \;\text{kg}\,\text{m}\,\text{s}^{-1}$ (this is the momentum of moving water, after water hits target is stops and it's momentum becomes 0). The force acting from the target on water (and from water on the target) is:

$$F \times 1 \;\text{s} = 500 \;\text{kg}\,\text{m}\,\text{s}^{-1} \\ F = 500 \;\text{kg}\,\text{m}\,\text{s}^{-2} = 500 \;\text{N}$$

This is about a weight of $50 \;\text{kg}$ object.

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