In two hours it will have moved 200 miles, etc. Similarly, if something is accelerating at a constant rate, the velocity will increase proportionately. Think about it, if your car is accelerating at 10 miles per hour per second, then if you were standing still, after one second you'll be going 10 miles per hour. Now fire the cannonball from the north pole, at watch it as it heads south. V miles per hour.
Lets say the Earth is rotating at w revolutions per hour.
Thus we see that the acceleration, and hence the force on the cannonball is proportional the speed of rotation of the Earth, and the speed of the object that is moving relative to the Earth. Now lets apply this formula to bathtub drains. In comparison to the other forces at work in a draining bathtub, this is almost insignificant, and no experiment that you could do on a cruise ship or in your bathtub could detect a force of this magnitude. The water near the drain is already gone in a matter of a second or less, so there just isn't any time for a force of this magnitude to do any real work on the water. This effect has been demonstrated under laboratory conditions, but the amount of care taken to eliminate outside disturbances is very great.