Hydrodynamics Bernoulli's equation

[Gyroscope]

Homework Statement

The water supply of a building is fed through a main pipe
6.00 cm in diameter. A 2.00-cm-diameter faucet tap, located
2.00 m above the main pipe, is observed to fill a 25.0-L
container in 30.0 s. (a) What is the speed at which the water
leaves the faucet? (b) What is the gauge pressure in the
6-cm main pipe? (Assume the faucet is the only “leak” in
the building.)

Homework Equations

The Attempt at a Solution

a) is easy.

Flux=Av

b) Apply Bernoulli's. I understand how to solve. But it rises a question: The energy associated with pressure is being converted in potential energy per volume when the water ascends to the faucet, so that the kinetic energy per volume is constant? Is this true?

 

[Chi Meson]

Your observation would be true for (i) an incompressible fluid that (ii)goes through a pipe with constant diameter. Regarding (i), water is treated as an incompressible fluid for these types of problems. THe diameter of the pipes chage, so speed changes and therefore KE changes.

 

[Gyroscope]

Yes, it is what I meant. So if the pipe has constant diameter the water will ascend at constant velocity?

 

[Chi Meson]

That's the "flux". If the volume flow must be constant, and the x-sectional area is constant, then the speed must be constant.