[chris (OP)]

A question that came in to the "Ask! The Naked Scientists" radio programme / podcast today was:

"If I hold a hose firing out water, I can feel the force of the water coming out. If I hold the hose underwater, it feels a lot less. Why?"

I explained that the force you feel as the holder of the hose is Newton's 2nd and 3rd Laws (F=ma, and reaction force). I also said that, if the rate of the water leaving the hose in both conditions is the same, then the force should be the same, so I doubted the observation.

Instead, I speculated that the position in which the hose was being held may well be different in both conditions, which may lead to a subjective difference in the experience. Specifically, a hose watering the garden is more likely to be held horizontally, while a hose held into a swimming pool is likely to be more vertical, so the water back-pressure is doing work lifting the hose against gravity, meaning that the force component exerted on your arm is less.

Am I right?

[evan_au]

Another difference between a hose in air and a hose underwater is that:
- In air: You must support the weight of the hose and the water inside it, plus the reaction force
- Underwater: The hose+water has close to neutral buoyancy, so you only have to support the reaction force

[RD]

... if the rate of the water leaving the hose in both conditions is the same ...

I don't think that will be the case: air-resistance is trivial compared to water-resistance,
which will reduce flow from the hose, and consequently less reaction force.

There's also hydro-static force reducing flow from the hose,
( the deeper the hose is held underwater the greater that will be).