Fluid Mechanics- Bernoulli Equation

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SUMMARY

The discussion centers on the application of the Bernoulli Equation to non-uniform flows, specifically examining the velocity profile of water exiting a pipe with a parabolic velocity profile into a free jet. Participants debate whether the velocity profile remains parabolic or becomes uniform upon exiting the pipe. It is established that the absence of friction from air does not alter the velocity profile, but the flow path changes when the fluid exits the orifice, potentially affecting the profile. The consensus leans towards the idea that the velocity profile may not remain parabolic due to changes in flow dynamics at the exit.

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  • Understanding of the Bernoulli Equation and its applications
  • Knowledge of fluid dynamics, particularly non-uniform flow behavior
  • Familiarity with concepts of velocity profiles in fluid mechanics
  • Basic principles of incompressible fluid flow
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  • Research the effects of orifice flow on velocity profiles in fluid dynamics
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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.
 
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