How high can water rise in a stream when a hand is placed in it?

AI Thread Summary
The discussion centers on the physics of water displacement when a hand is placed in a stream. It references Bernoulli's principle to analyze how the water's speed and pressure relate to the height it can rise on the arm. The conversation highlights the importance of the arm's angle and the need for mass conservation principles, including the stream's cross-sectional area. Participants express uncertainty about the calculations and seek clarification on whether the hand is submerged or not, which affects the application of Bernoulli's principle. Overall, the thread explores the theoretical maximum height water can rise based on kinetic energy conversion.
SimbaTheLion
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"If you put your arm in a stream flowing at U metres per second, how far can water rise up it?"

Not really sure if what I'm doing is right. Presumably it depends on the angle of your arm in the water. If we let the speed of the water at your arm be V, we get, by Bernoulli, taking the height up your arm to be h, the pressure to be p_atm before and p afterwards:

p_atm/ρ + U²/2 = p/ρ + V²/2.

And we know p = p_atm + ρgh.

Which gives:

U²/2 = gh + V²/2.

I'm trying to use mass conservation now, but then don't we need the cross-sectional area of the stream, and the area that is occupied by your arm?

Am I going about the question in completely the wrong way?

Help please :) !
 
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If all of the kinetic energy in the moving fluid were converted to potential (by increasing elevation) how high could it go?
 
gmax137 said:
If all of the kinetic energy in the moving fluid were converted to potential (by increasing elevation) how high could it go?

Well, suppose the fluid had kinetic energy E = mU²/2. Then we need to find h such that mgh = mU²/2. So h = U²/2g. Is that all I have to do? :S
 
Is the hand in the stream or out of it?

If it's in, there there's sense to apply Bernoulli's principal...otherwise it's simple force resolution.

I think.
 
dE_logics said:
Is the hand in the stream or out of it?

If it's in, there there's sense to apply Bernoulli's principal...otherwise it's simple force resolution.

I think.

Yeah, the hand is in the stream. Hmm, so is what I've done in the first post correct? If so, how do I continue?
 
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