Hydrodynamics Bernoulli's equation

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Homework Help Overview

The problem involves the application of Bernoulli's equation in the context of fluid dynamics, specifically examining the flow of water through pipes of varying diameters and the resulting effects on speed and pressure. The scenario includes a main pipe supplying water to a faucet located above it, with specific measurements provided for analysis.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between pressure, potential energy, and kinetic energy in the context of fluid flow. Questions arise regarding the assumptions of incompressibility and the implications of changing pipe diameters on water speed and energy conservation.

Discussion Status

The discussion is ongoing, with participants exploring the implications of fluid dynamics principles. Some guidance has been offered regarding the assumptions of incompressibility and the behavior of fluid flow in pipes of constant diameter, but no consensus has been reached on all aspects of the problem.

Contextual Notes

Participants are navigating the complexities of Bernoulli's equation and its application to a real-world scenario, with specific attention to the assumptions made about fluid behavior and the setup of the problem.

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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?
 
Last edited by a moderator:
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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.
 
Yes, it is what I meant. So if the pipe has constant diameter the water will ascend at constant velocity?
 
That's the "flux". If the volume flow must be constant, and the x-sectional area is constant, then the speed must be constant.
 

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