Fluid Mechanics- Bernoulli Equation

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Discussion Overview

The discussion centers on the application of the Bernoulli Equation to non-uniform flows, specifically examining the velocity profile of water flowing through a pipe with a parabolic velocity profile as it exits into a free jet. The participants explore the effects of fluid dynamics and potential changes in velocity profiles due to external factors such as air friction.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes that the velocity profile of water exiting a pipe with a parabolic profile remains parabolic in the absence of any forces acting on it.
  • Another participant challenges this view, stating that the flow path of a fluid changes when it leaves an orifice, suggesting that the velocity profile may not remain parabolic.
  • Some participants mention the complexity of the situation, noting the interaction of two fluids and the absence of air friction affecting the water.
  • A later reply assumes the incompressibility of water to further the discussion on the velocity profile.

Areas of Agreement / Disagreement

Participants express differing views on whether the velocity profile remains parabolic after exiting the pipe, indicating a lack of consensus on this aspect of fluid dynamics.

Contextual Notes

The discussion involves assumptions about fluid behavior, such as incompressibility and the effects of external forces, which remain unresolved and may influence the conclusions drawn.

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The Bernoulli Equation for non-uniform flows have a constant at the kinetic energy term which describes the velocity profile at that place. The problem is this, If a have water flowing through a pipe with a parabolic velocity profile and then the water exit the pipe at free jet and there is now friction due to air, what would be the velocity profile at the free jet area, uniform or parabolic?
There is nothing in between these two points that would accelerate or deccelerate water.

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I don't think there is a simple formula for that, sorry. You have two complex fluids moving relative to each other.
 
Cyrus said:
I don't think there is a simple formula for that, sorry. You have two complex fluids moving relative to each other.

There is no friction from the air on the water.

Here is what I think, since there is nothing that would affect the velocity profile of the water, water would continue to have a parabolic profile. But that's what I think, what do you guys think?
 
No that's not true. When a fluid leaves an orifice its flowpath changes. It can expand or contract at the exit.
 
Ok then, that's very true but let assume that water is incompressible.
 
Last edited:

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