Why water moves in a pipe like a small whirlpool?

I had often noticed when a road is filled with water. And when water moves into a small pipe it moves in a rotating way not straight, it forms a small whirlpool likewise.

I don't why does that happen, as to my knowledge water should go straight into pipe not by forming a small whirlpool.

• One of the reasons, perhaps is the viscosity. The water on the boundary, experiences more resistance, and has lesser speed. The water in centre of pipe experiences lesser resistance to flow. Flow Speed is maximum in the centre. This is typical flow pattern of fluid in pipe – Tojrah Jul 9 at 13:42
• The direction is also dependent on whether you are in the north or south hemisphere.. – user207455 Jul 9 at 13:49
• @SolarMike That's a myth... the Coriolis force is way too small at the scale of a storm drain/toilet/sink. It depends on what the initial spin is that gets stretched out. On the scale of hurricanes or whirlpools in natural bodies of water, the Coriolis force may come into play, however. – tpg2114 Jul 9 at 14:07
• @tpg2114 so why if I swirl the water one way in my sink it continues and if I swirl it the other it stops and reverses? Or are you suggesting I used the wrong hand (like the left)... – user207455 Jul 9 at 14:11
• @SolarMike If your drain is perfectly symmetric, it can only spin one way no matter which hemisphere you are in. Look at the equation in my answer -- if the water is swirling counter-clockwise, the vorticity vector is opposite the velocity gradient vector. So the swirl will slow, stop, then swirl the other way. If the initial swirl is clockwise, the vectors are aligned and it will begin to swirl faster. It is, of course, possible to force it to swirl other directions through drain design or water injection differences (like in a toilet bowl). – tpg2114 Jul 9 at 14:36

The mechanism is called Vortex Stretching. Imagine a small, flat pool that is gently swirling around. It doesn't have to be much vorticity, but there has to be some rotation in it somewhere. This is usually due to turbulence and a few other things, but it's not terribly relevant so long as there is some rotation happening at some scale.

This means there is vorticity in the pool. Vorticity is defined as the curl of the velocity, or $$\mathbf{\omega} = \mathbf{\nabla}\times\mathbf{u}$$, where $$\mathbf{u}$$ is the velocity vector. When you open a plug, say in a toilet or bathtub, or it encounters a drain and can fall into it, any existing vortices get stretched out along the direction of the drain. If you imagine our flat pool and you suddenly open a hole in the bottom of it, the water can accelerate into the drain and so it is speeding up in the direction of the drain.

When you have a vortex and begin pulling it along its axis, the vortex will get narrower and spin faster. This is due to conservation of angular momentum. It's the same reason that a figure skater spins faster when they pull their arms closer to their body, and spin slower when they move their arms away from their body.

We can actually put an equation to this. The vorticity equation is derived by taking the curl of the momentum equation. For an incompressible, inviscid fluid, you end up with:

$$\frac{\partial \mathbf{\omega}}{\partial t} + \mathbf{u}(\mathbf{\nabla} \cdot \mathbf{\omega}) = (\mathbf{\omega} \cdot \mathbf{\nabla})\mathbf{u}$$

The first term on the left is the time rate of change of vorticity. The second is the change in vorticity due to it being moved around by velocity. The term on the right hand side is the vortex stretching term. It says that when the vorticity axis is aligned with the velocity gradient axis, the vorticity changes. This is what causes the whirlpool to spin up in a drain.

• you means water has rotation due to turbulence so, if we drain water in vacuum then it will not make a whirlpool. – GameChanger Jul 9 at 15:48
• @GameChanger Vacuum has nothing to do with it -- it's turbulence within the water. If you were to fill a tank of water and keep it really really still for a long time, long enough for all motions inside it to die out, and then you were to pull the plug on it, it would not form a vortex. I have seen a video of that in a fluids lecture years ago, if I remember who did it, I'll post it. It might have been from the National Committee for Fluid Mechanics films. One of the vorticity films perhaps, or the rotating flows one. – tpg2114 Jul 9 at 16:03
• Ok, thanks for helping me. – GameChanger Jul 9 at 16:06
• You will notice that water always rotates one way when going down a drain (in a given hemisphere). Implicit in the explanation above is some kind of spontaneous symmetry breaking where, depending on the initial distribution of vorticity in the fluid, it rotates sometimes left, sometimes right under the influence of vortex stretching when going down a drain. However this does not happen: gravity dictates the direction, at least when there is only a small amount of net initial vorticity in one direction or another in the fluid (in the absence of forced rotation, for example). – jamesoh Jul 10 at 7:18