If the pipe has constant cross sectional area and if the fluid is incompressible (water is NOT squishy) then the velocity is the same at every section of the pipe since there is no place to store water along the pipe. That is what continuity means. Yes, A1V1 = A2V2 but since A2 = A1 then V2 = V1.
Now of course if the pipe is higher, the velocity will go down unless the pump works harder. That does not change the A1V1 = A2 V2 so V2=V1. It is just a different V at both point 1 and point 2 along the pipe. In other words less water flows through the higher pipe, everywhere along the pipe.
Hi!
I'm having a hard time figuring out if flow rate decreases when water goes up a vertical pipe. I know that at some point when the water can't be pushed any higher due to P=pgh, the water stops flowing from the pipe. I also believe that due to continuity, all sections of the pipe should have the same flow rate no? I have seen many people calculate the second velocity for the Bernoulli equation using the continuity equation A1V1=A2V2 assuming constant flow rate. Is that really practical in real life though? Wouldn't a pump have to have a variable output or something to maintain the same flow rate while pumping water in a vertical pipe higher and higher? I guess I'm a little confused on the subject and I really hope someone can clear it up for me. Thank you for your help!!
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