Forces on a string
My statics is a bit rusty so I'm hoping one of you can help me build an equation. And no, this is by no means homework.
If you have a string (let's allow the thickness of which to be a variable - but we can go with just a coefficient of drag I suppose) and you attach it to the bottom of a stream (or small river). After stretching it strait up out of the water with your fingers and holding it still, what force are you pulling up with, to keep the string steady (and let's assume the rate of flow, of water, past the string remains constant)? The mass of the string can be neglected I suppose but it would be nice if we included it.
Essentially, I'm wondering if the force on your hand changes as you move your hand up the string. Is the force different on your hand when it is near the water vs. when it is holding the string farther up?
I'd like to be able to say what happens to that force as the coefficient of drag changes, or the flow rate, or the percentage of the string out of the water vs. in the water, or even the density of the fluid.
If you have a string (let's allow the thickness of which to be a variable - but we can go with just a coefficient of drag I suppose) and you attach it to the bottom of a stream (or small river). After stretching it strait up out of the water with your fingers and holding it still, what force are you pulling up with, to keep the string steady (and let's assume the rate of flow, of water, past the string remains constant)? The mass of the string can be neglected I suppose but it would be nice if we included it.
Essentially, I'm wondering if the force on your hand changes as you move your hand up the string. Is the force different on your hand when it is near the water vs. when it is holding the string farther up?
I'd like to be able to say what happens to that force as the coefficient of drag changes, or the flow rate, or the percentage of the string out of the water vs. in the water, or even the density of the fluid.
ASKER
The force of gravity will cause an increasing force simply because of the mass you are holding up increases. However, that same increasing mass is working against the current, or flow, of water. When you are an inch off the water you are feeling just the pull from the current with very little due to gravity. But If you pay out a mile of rope, chances are the mass of the rope is now most of what you are working against, not the current. How much of the force is due to current flow and how much is due to gravity at any given length?
Also, the geometry must be considered. An infinite amount of force is required to get the rope to run perfectly vertical. There will be a slight bend in the rope due to the flow. When pulling softly on the rope, you may perhaps overcome the drag of the current and keep the rope in the air, but there will be more bend, or angle away from vertical (normal) at the bottom of the river compared to pulling with a stronger force. This angle has quite a bit to do in the equation (like a man standing on a tightrope).
Also, the geometry must be considered. An infinite amount of force is required to get the rope to run perfectly vertical. There will be a slight bend in the rope due to the flow. When pulling softly on the rope, you may perhaps overcome the drag of the current and keep the rope in the air, but there will be more bend, or angle away from vertical (normal) at the bottom of the river compared to pulling with a stronger force. This angle has quite a bit to do in the equation (like a man standing on a tightrope).
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Thanks d-glitch. I appreciate your jumping in. Coming at it from that approach I would expect an FE analysis to show the force lessening as it becomes more vertical. And this because it gradually is exposed to less flow of water. The segments would need to become smaller, or fewer in number, as the rope "stands up".
I'll conduct an experiment and let you both know what I find. Thanks for the effort so far.
I'll conduct an experiment and let you both know what I find. Thanks for the effort so far.
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BigRat, I agree with you that the force won't change as one moves a hand up the string (ignoring the mass of the string) if the string has zero change in its geometry. This is something I'll just have to experiment with and I'll try to post the results here.
Until then, I think I better hand out some points.
Until then, I think I better hand out some points.
ASKER
Thanks all...more to come.
ASKER
Thanks!
To the first approximation. it does not.
If you do not neglect the mass of the string, it goes up a bit.
"I'd like to be able to say what happens to that force as the coefficient of drag changes, or the flow rate, or the percentage of the string out of the water vs. in the water, or even the density of the fluid. "
with all these things it goes up
How much depends on all the factors listed.
Actually if you insist that the string be vertical, the force approaches infinity.