Can anyone explain the physics behind a whirlpool?

[michaelsqin]

Can anyone explain the physics behind a whirlpool? If I stir water fast enough, why do water molecules have a tendency to go to the edge of the container? I think rotational momentum might be involved but don't understand how.

 

[giann_tee]

Its the centrifugal force keeping them to the edge.

 

[michaelsqin]

Can you elaborate? My teacher told me only the centripetal force is real.

 

[MarcusAgrippa]

Can you elaborate? My teacher told me only the centripetal force is real.

Identify your reference frame first. If you want to use Newton's laws, you must choose an inertial frame. So choose the inertial frame in which the container is stationary. In this frame, once the steady state has been established, the water molecules move with circular motion around the axis of rotation of the whirlpool. In circular motion, the force needed to make a particle move in a circle with uniform motion is centripetal, not centrifugal. "centripetal" tells you the direction of the force; it does not identify physically what force is acting. In the case of the fluid, consider a small element of fluid mass and follow it in its motion. The forces acting on it are gravity, which is irrelevant to your question as it acts vertically and not horizontally; and contact with the surrounding fluid. This contact force per unit area of surface of the fluid element is called pressure. The pressure changes with distance from the axis of rotation in the rotating fluid, being greater as you go out further from the axis, and getting smaller as you get closer to the axis. The difference of pressure on the outer and inner surfaces gives rise to a nett force toward the axis of rotation. This is the force that keeps the fluid element moving in the circular path. As you get closer to the axis of rotation at a fixed horizontal level, the pressure might drop to zero at a finite distance from the axis, and its then becomes negative. Negative pressure means that the fluid is in tension and, since fluids and gases (unlike solids) cannot sustain large tension without the molecular bonds breaking apart, the fluid tears apart and cavitates, leaving the centre of the whirlpool empty of fluid.

Of course, when you begin to stir the fluid, the pressure starts off uniform throughout the fluid and so is not able to supply the force needed to keep the fluid elements in circular motion, so initially the fluid particles move outwards. Why? Not because a force is acting on the to puul them outwards, but because NO FORCE is available to push them inwards. Think of it like this: imagine the fluid element without the surrounding fluid. You give it a finite velocity with your spoon. What will it do after you stop pushing on it? It will continue with uniform motion in a straight line - because there is NO force on it! It will thus move out to the edge of the cup until the cup exerts a force on it which then forces it into a circular motion. The situation with the rest of the fluid around is more complicated, but similar: the fluid element does not move under the action of zero force, but the force initially is still not enough to force it into a circular motion, so it spirals out towards the edge, not because there is a force acting on it, but because the centripetal force on it is not strong enough yet to make the motion circular.

The idea of a centrifugal force is a fiction. It does not exist. It is a delusion suffered by a non-inertial observer who thinks himself to be inertial and tries to explain what he sees by the action of forces and using Newton's laws. But he is wrong, because his frame of reference is not inertial and so Newton's laws do not apply. To see this, imagine yourself on the wall of a spinning drum (like a centrifuge, or the fly-on-the-wall amusement park ride), and spinning with the drum. For good measure, imagine this spinning drum is in empty space away from all gravitational fields - this way you don't have to worry about gravity, which doens't add anything to the understanding of this problem. Imagine an object released inside the drum with a finite velocity in the plane perpendicular to the axis of rotation. It will continue with uniform motion in a straight line because there is no force on it, and so it starts to approach you who is on the wall. To you, it looks as if it is accelerating toward you (it is, in fact, accelerating relative to you!), and so you say: it is accelerating, and therefore there is a force on it pushing it towards me. But you are wrong. There is no force on it. However, there is a force on you, centripetal, pushing you inwards and accelerating you. That is why the object is accelerating relative to you.

 

[michaelsqin]

wow, thank you. The second and third paragraph are very clear and I understand. But I am somewhat lost on the pressure idea. It makes sense that the difference in pressure is creating the centripetal force, but for pressure to originate doesn't there have to be another force (because pressure = F/A)?

 

[MarcusAgrippa]

wow, thank you. The second and third paragraph are very clear and I understand. But I am somewhat lost on the pressure idea. It makes sense that the difference in pressure is creating the centripetal force, but for pressure to originate doesn't there have to be another force (because pressure = F/A)?

How one answers this one depends on one's point of view, i.e., macroscopic or microscopic. Macroscopically, pressure is an "internal" stress. It is the (normal) force per unit area exerted on the surface of a fluid element by the adjacent fluid elements, or by the boundary surface, if your element is in contact with the boundary. As regards "another force" causing the pressure, I am not sure what you have in mind, but let me try to guess. The motion of a small element of fluid is determined only by the forces acting on that element. These forces are of two types: 1. those exerted by force fields (sometimes called "body forces") like gravity or the electromagnetic field if the fluid consists of mobile charges as in a plasma (magnetohydrodynamics), and 2. those exerted by contact. Since these are proportional to the area of contact, it makes sense to use force densities (i.e. force per unit area) to describe them, These are called internal stresses, and include pressure and shearing stress. In the simplest model of a fluid, we assume that there is no shearing stress, so that leaves only the normal contact force, due to pressure. Of course, how the internal stress is caused physically is a different question. The fluid may being pushed by a distant boundary, or something else, which stresses the fluid next to the boundary, which stresses the fluid next to it, and so on. But in the final analysis, the distant boundary does not exert any force on an element of fluid internal to the fluid - which is what you appear to be thinking. Think of a pile of books, and push the bottom one. Why does the top one move? Not because you are pushing it: your hand has no contact with the top book. The top book moves because of the forces exerted on it by those books that make contact with it. So it is the the friction exerted by the adjacent books that make the top book move, not your hand. Analogously with the fluid: the only forces on a given element are the body forces and the force due to the pressure of the adjacent fluid.

Not very clearly explained, but that is the idea.

 

[michaelsqin]

thank you again. I think I understand it now, and I'll re-read this in a couple of days to make sure.