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Like the volume flow rate i understand A1v1=A2v2

for example i was doing this problem : https://www.physicsforums.com/showthread.php?t=80584

Well its inversely proportional right but (im just being stupid probably because I'm really tired) but if A2 is 1/4 the size of A1 for example, then v2 is going to be 4 x the size of V1? like

A1v1 = 1/4A2v2 so 4A1/v1 = A2v2 then v2 = 4(A1/A2)(v1), well like in the problem i linked, what happens to that A1/A2? why does it disappear when being plugged into bernoulli's equation?

Also another question is the A = cross sectional area right? what's that even mean like is that the same as surface area, or regular area, or what? because in a problem like this https://www.physicsforums.com/showthread.php?t=65810 (now I am not sure if the member solved it 100% correct) but the person here puts Volume Flow Rate = pir^2v1 for example, what is the volume flow rate in this case i don't understand and is A just the area of a circle on the tube , even tho its open its not used like a cylinder's area?

thanks if anyone can help me out I am like brain dead at the moment.