# Fireman with a firehose scenario

engkyq
Hi, this is my first post and am trying to answer the following scenario out of a general curiousity.

Scenario:
Suppose a firemen is standing in front of a doorway with a firehose.
He then points the nozzle of the firehose at the doorway a foot behind the door frame
He then turns on the water to a level where he is barely able to keep from being pushed back by the water exiting the nozzle.
The door is then closed and the water is hitting it at a foot distance from the nozzle.

Question:
Will the fireman experience more force pushing him back with the door closed than with the door opened? If yes, what are the laws to explain this?

Thanks!

Gold Member
Welcome to the forums!

It depends, he will not experience a different force outside of stray water bouncing back and hitting him. However, with a fire hose at 1ft away, that would be a very significant force, but if you move a few feet back, the fireman will not feel much water bouncing back and hitting him. The important point is, however, that the water ejects with a force that is completely independent of what is infront of it.

The force of the water comes from Newton's third and 2nd law. The water going through a nozzle will have its velocity increased since the area of the opening becomes smaller. This change in velocity creates a change in momentum which translates into a force that accelerates the water. Now the third law says that an equal and opposite force will be felt, and in this case, it would be onto the fireman. However, that is where the forces stop. They are not dependent on what happens to that water once it leaves the nozzle.

maze
I'm not sure, but my inclination is to say that, if the rate of water ejection is constant (ie: the flow rate is not affected by the nozzle being close to the door) then there will be no extra force. My reasoning is that the force is the rate of change of momentum, which is proportional to the rate at which water is ejected out of the hose.

I would alos be interested to hear from someone more knowledgeable.

There will be no extra reactive force on the nozzle. As stated above, there could be some extra force if there is water bouncing back and hitting the fireman, but that seems to be a separate issue from the main question.

maze
I'm not so sure. If the hose was, say, a tenth of a milimeter from the wall, then I'm pretty sure that it *would* be different from if there was no wall there. So at some point it has to be a question of degree.

engkyq
Thanks for the responses!

I'm only interested if the nozzle will feel additional force pushing it back once the door has closed. Assume a scale is attached to the nozzle, perpendicular to the doorway, to measure the force that is pushing it back. To expand on the scenario, after the door has closed, let's move it towards the nozzle until it touches it.