does Spiral motion increase velosity ?

Question

i was wondering if you pour water down a spiral column, does it get faster than if the same water was to flow down a straight vertical drop?

ok, so the spiral is not faster. thanks

Answer 1

Imagine that we have a tall circular tower that was clear space inside, except that there's a spiral staircase on the inside wall, and there's a racetrack for a ball. Imagine that I am at the top of the tower, and I drop 2 balls, one straight down the clear center of the tower, the other on the spiral racetrack. Which ball would you bet on getting to the bottom first? That should answer your question.

Addendum: In response to critifcism of this analogy, even in a FRICTIONLESS system, the velocity of the ball is solely dependent on the drop in elevation, which means that at any given height, both balls are going at the same speed. But the spiralling ball has to travel a LONGER distance, hence it will take a longer time. Pick up a book on classical mechanics and actually do the math.

This analogy assumes that the water spirals in a classic whirlpool pattern where there's a clear tunnel through it. It does not drain faster, unless it's draining into a closed chamber, in which case it permits air to escape. Such a non-turbulent flow would be faster than a turbulent cross-flow of air and water. This is a typical "fluid flow problem" that process engineers frequently have to face.

Addendum: Archknight, the whole point of classical Hamiltonian mechanics is that energy is conserved. After both balls have dropped height H, assuming that they both started at rest, both would now have kinetic energy = mgH, where m is the mass of the balls, g is the gravitational acceleration, and H is the height dropped. From this we can calculate their velocity in the direction of their travel

mgH = (1/2)mv²
v = √(2gH)

However, the ball falling straight down has a shorter distance to travel to drop H in height, while the ball rolling (we'll ignore rotational inertia, since that would only slow it down further) has a longer distance to travel to drop H in height. The ball on the spiral racetrack will lose every time to a ball dropped vertically. As a matter of fact, Bernoulli's principle used in hydraulics states that in gravitationally induced smooth fluid flow, the velocity of the flow is √(2gH), and I'm making the simplifying assumption that whirlpool flow is similiar to smooth spiral flow, which I think was the point of this question.

Answer 2

To be perfectly technical, the velocity of a drop going down a spiral is identical to the velocity of the drop going straight vertically done. Velocity is path independent and since it is spiraling, it is only making progress in one direction and that is down. They will reach the bottom at the same time (assuming negligible resistance). If there is resistance, the shorter path (vertical) will be the fastest. Now, if you are talking instantaneous velocity, then it will be higher in the spiral than the vertical drop, but it is counter productive as it just counters itself going in a circle. The speeds in up-down direction will be identical (neglecting resistance) no matter the path.

Oh, and to address the analogy of the answerer #1. Unfortunately, a ball rolling around a circular track transfers a considerable amount of energy into rotational motion which takes away from its vertical descent. If you had an ideal fluid, they would fall at the exact same speed. But now you are introducting rotational kinematics which is completely irrelevent to the original question.

Okay.... I will try to break down the classical mechanics for you since you seem to be mistaking speed for velocity. Velocity is path independent while speed is path dependent. The velocities are in fact equal. The velocity of any object engaged in circular motion is ZERO. That is because it isn't actually making any progress. It's speed may be anything, but the velocity is zero. Something moving in a spiral only has velocity downward in the Z-direction, there is none in the X-direction or Y-direction. Because the velocity is dependent upon gravity, it will be equal to that of the object taking a different path. The whole point of defining velocity is that the PATH DOES NOT MATTER. That is exactly what classical mechanics says.

If that wasn't good enough, we can do it by conservation of energy. Potential energy is mass times acceleration due to gravity times change in height. Kinetic energy is half the mass times the VELOCITY of an object, squared. As each object changes in height, both velocities will change together. The two will always have the same velocity.

As the water goes down the spiral, it will have a higher speed then the vertical drop simply because it is running in circles but also falling at the same velocity. But that speed is really meaningless as it does no work. The two streams of water will travel the same distance in the same amount of time.

You can apply gravity or conservation of energy. it still comes out exactly the same. There is only one hang up. Conservation of energy also includes energy lost to resistance of some sort. It will be either friction (or heat) or just turbulence in the fluid (thermodynamics refer to this as entropy but you dont need to know anything about thermodynamics to know that frictions slows things down). The exact nature of this resistance is irrelevent. If this was a question about fluid dynamics, you could then begin to make an argument about how the longer path gives more opportunity for energy loss and thus slows it down. If this were just a straight classical mechanics energy question, you would ignore the nature of the fluid and say they fall at the exact same speed. I am not sure what you are asking but this is the exact nature of the problem. I am sorry answerer 3, but I am still having a hard time understanding you. But regardless, this is what physics says about the problem.

Answer 3

in short it rather is genuine this is all right down to gravity, even you have gravity, besides the fact that if or no longer this is totally small, each and every thing from a rock, to a planet attracts one yet another in accordance to the tension of gravity. in case you initiate from earth, the moon orbits the earth, the earth orbits the solar. each and every of the planets in our image voltaic device orbit the solar and then our solar is likewise in spinning around the Milky way. each and every of the 300 billion starts you point out additionally are spinning around the milky way. maximum scientists have faith there's a black hollow on the centre of the the Milky way. Black holes do no longer emit mild, it rather is a great gravitational tension which you would be able to sense its result yet isn't seen. It would not consistently must be a black hollow although, evaluate a dance significant different, you stand table sure in the centre of the room and he or she/he strikes in the direction of you with speed and grabs and pulls on your hand, the prompt result's you will rotate and in the experience that your rapid adequate you swing around. Now think of this isn't any longer an significant different yet 2 planets, or 2 image voltaic device each and every exerting gravity entering each and every others course. you will see how the rotation can turn up without the will for a black hollow.