The rotation is grossly balanced by the pressure gradient force (inwards) and the centrifugal force (outwards). The rotation can be in either direction to be balanced in this way. The Coriolis force, which would have a latitudinal dependence, is too small to play a role in this force balance. Friction, which is also small compared to the first two forces, but big enough to  dissipate the kinetic energy and eventually stop the the rotation. 

This is a myth.  The Coriolis forces require very large bodies to play a role, not buckets or toilets.  Otherwise the rotation is determined by surface and shape properties of the container and the hole itself or initial data.  You can typically get it go either direction with an initial push.  

Not clockwise necessarily, can made anticlock wise too, it depends on the twist, of thread of jute/plastic, when rope is made. Bucket  would not rotate, if it pulled by strip or solid rope.

It can be even in anti-clock wise depends on the geographic location also..,  

The rotation is grossly balanced by the pressure gradient force (inwards) and the centrifugal force (outwards). The rotation can be in either direction to be balanced in this way. The Coriolis force, which would have a latitudinal dependence, is too small to play a role in this force balance. Friction, which is also small compared to the first two forces, but big enough to  dissipate the kinetic energy and eventually stop the the rotation. 

No idea why 4 people downvoted Ramprashanth's correct answer above ???? Unbelievable ....

The Coriolis force responsible for the eddy's spin direction works out exactly oppositely in the Earth's Northern and Southern hemispheres, so that liquids spin down clockwise in the North (say, the UK or US or France) and anticlockwise in the South (say, Australia or Argentina or South Africa)

The contribution is down-voted possiby because the answer is not quite correct as the Coriolis force is not relevant in this type of movement. Coriolis forces come into play once the Rossby number Ro = U/(fL) is near 1 or lower. U is the velocity, L is the length scale and f is the Coriolis parameter. In a bucket with rotating water the scales are typically U = 1 m/s, L = 0.5, f is 10^-4/s, so that Ro ends up to be > 10^4, i.e. Coriolis force is negligible. Even upon initiating a rotational movement in a bucket the Coriolis force cannot play a role,as it is present only if U > 0 and would then act perpendicular to the movement and not steer the rotation in one particular direction.

The body of water has a net angular momentum associated with the Earth's rotation which we interpret as the Coriolis force.  If one drains the tub out the center then the angular momentum remains in the tank and it speeds up. http://www.nature.com/nature/journal/v196/n4859/abs/1961080b0.html

This is not the only effect at play here.  Even for a nonrotating system, drains induce vortices and net angular momentum must be conserved.  

A further thought on the initial movement: if the water is accelerated purely radially by the pressure gradient force and there is no rotation yet, the Coriolis force, while acting perpendicular to the velocity, will trigger a movement perpendicular to the radial direction. If other forces are absent or still small this initial movement could determine the direction of the rotation. Once the rotation is established the centrifugal force takes over and governs the balance with the pressure gradient force. However, this requires ideal start conditions where acceleration is purely driven by the pressure gradient force.

How can you get radial pressure gradient if it is not rotating? Do you mean rotation in the drain?  Are you talking about spinning up the whole fluid from rest?  

Peter,

I have spent years of my life in the Southern Hemisphere and years in the Northern hemisphere. I can assure you that in the South, water always drains from a simple kitchen or bathroom sink anticlockwise, and in the North, it always does clockwise. I think that was the question put here, no ifs nor buts. Your answer seems to be addressing other scenarios.

@Clifford: when water falls through the hole it displaces the vertical column above the hole, which in turn creates a radial pressure gradient and a corresponding force.

@Chris: can you explain your observations and why I have observed clockwise whirls in the N hemisphere? Have you made observations at the equator as well - which direction would one observe there?

As you well know Peter,

it depends on how far you are from the Equator, and on whether there are other elements involved (such as the above-cited 'initial push', etc.) For a straightforward smooth sink or bucket situation, far enough from the equator (where close, small extraneous elements may play a determinant role), then the situation is reliably as described.

It seems that for some reason we're all talking at cross-currents but actually saying the same thing - to wit, that in the absence of other forces, even small effects play the key role. This works both ways - in the absence of anything else, even a small Coriolis force will provide the determinant initial boundary impetus

I just tried it in my a tub a couple of times and it wend the "wrong" way.  Maybe I'm too close to the Bermuda triangle.  

@Peter, that seems like a VERY small force!