Care to explain which is right and why? I also thought that the water in the smaller tube would be faster and have more pressure, causing there to be more water in tube B.
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Just a crude drawing.....
Ummmmm I'd love to but I've just realised that my F1 car venturi analogy was incorrect.. that's more like a narrow pipe going to a wide pipe! So I'm not actually sure why A is the correct answer for the pipes. It does mean that the pressure is higher in the wider pipe, but I can't say why. Someone earlier mentioned something about the water speeding up under B, and the resultant reduction in pressure being due to that, and that sounds about right, but I can't actually picture the mechanics behind that.
EDIT: but, this might work:
It may be analogous to roadworks on a motorway, where three lanes have to filter into a single lane. In the three lanes, you have lots of cars in close proximity, all wanting to to travel down the single lane but getting eachother's way, so there is a high concentration of cars before the restriction - i.e. higher density upstream of the pipe reduction. Once you get onto the single lane, things spread out again. You go faster and spread out to a natural comfortable distance from the traffic around you, hence lower pressure downstream of the restriction.
So, in the pipe system from the question, you have a force causing the water to travel from the left to the right. The water obeys this force but meets the pipe restriction, so much of the force pushing the water through the pipe is used trying to press more water into the large pipe. More material in the same volume = higher pressure. This pressure pushes some water up pipe A and some into the reduced diameter pipe. Once the water reaches the reduced diameter pipe, it is free to go where it is pushed to. The restriction on its progress is reduced, so when you push at it, all the force goes into moving the water, none goes into attempting to compress it and raise its pressure, so its pressure reduces to meet a new, less stressed equilibrium. If the reduced diameter pipe is still completely full of water, then it will still be exerting some pressure on the pipe walls, and thus some water will be pushed up spout B, but not as much as A. I would guess that if you looked down into spout A this water would appear to be fairly calm, unless the pressure driving the whole system was fluctuating...
EDIT 2: Could it be explained by that gas equation... something like pressure = temperature x volume? Sorry... it's been 15 years since I studied fluid dynamics... Anyway, if that does apply, then you can perhaps treat the pipe before the restriction as a closed container of fixed volume. Add energy to the system, (like pushing against it) and the pressure increases. After the restriction, the container could be regarded as open, so the volume is not fixed. Add energy to that and the volume increases rather than the pressure.
Perhaps..
That's all guesswork, so don't quote me in your fluid dynamics exam...