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

[SimbaTheLion]

"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 :) !

 

[gmax137]

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

 

[SimbaTheLion]

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

 

[dE_logics]

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.

 

[SimbaTheLion]

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?