Imagine you're are out in the space observing a long pipe. First half of the pipe has Area that are larger than the area of the second half of the pipe. Further imagine, along the one end of pipe, a chuck of water(or a lot of water) is given a slight push to set in a motion at constant velocity along the pipe(No friction, No compression, Constant Density). Now, the water continues to move along the pipe all the way through and some part of the water now enters the second section of the pipe. Now, I have a trouble picturing what's gonna happen. I thought the mass of water must not change. So the amount of water getting out of the one section of the pipe must enters the other section of the pipe. In order to do that the water has to run faster along the section of pipe with smaller area. So now I have some part of the water running faster than before. Considering the water and pipe as one system, I can see that the energy is not conserved.(since the water now runs faster). But I can not find any source who could possibly do a work on the pipe and the water. For some reason I suspect that it has something to do with Bernouli's equation involving pressure. How should I make of this? It seems like here the Energy is not conserved. Help?