Bernoulli vs Energy Conservation?

Click For Summary

Discussion Overview

The discussion revolves around the comparison between Bernoulli's principle and the conservation of mechanical energy in fluid dynamics, particularly in the context of a tube with varying velocity profiles. Participants explore the implications of turbulence and frictionless flow on energy conservation equations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether it is possible to have the same velocities at both ends of the tube and how to construct the energy conservation equation in this scenario.
  • Others argue that mechanical energy may not be conserved if turbulence is present, suggesting that same velocities do not necessarily imply no energy loss.
  • A participant notes that the problem statement specifies "frictionless flow," which could affect the energy conservation analysis.
  • There is a discussion about the physical possibility of having the same kinetic energy at both ends of the tube, given a changing velocity profile.
  • One participant references the transient 1D momentum equation and its integration, which introduces additional terms alongside Bernoulli's terms, indicating a more complex relationship in unsteady flow conditions.

Areas of Agreement / Disagreement

Participants express differing views on the implications of turbulence and the conditions under which mechanical energy is conserved. The discussion remains unresolved regarding the relationship between Bernoulli's principle and energy conservation in this specific context.

Contextual Notes

There are limitations regarding assumptions about the flow conditions, such as the presence of turbulence and the nature of the velocity profile, which are not fully resolved in the discussion.

gamz95
Messages
23
Reaction score
1
untitled.jpg
In the example, is it possible to have same velocities at the two ends of the tube? How would you construct energy conversation equation?
 
Physics news on Phys.org
Why would you expect mechanical energy to be conserved if there is any turbulence involved? Same velocities doesn't imply no energy loss.
 
sophiecentaur said:
Why would you expect mechanical energy to be conserved if there is any turbulence involved? Same velocities doesn't imply no energy loss.
The problem statement does say "frictionless... flow."
 
  • Like
Likes   Reactions: sophiecentaur
gamz95 said:
View attachment 98068 In the example, is it possible to have same velocities at the two ends of the tube? How would you construct energy conversation equation?
It is shown right in the solution they gave. If you look at their final equation, it's just F = ma.
 
  • Like
Likes   Reactions: gamz95 and sophiecentaur
Yes it is indeed frictionless. Therefore, when normal energy equation constructed the KE1=KE2(Since it says that velocities are the same). However, how is this physically possible? And question gives a changing velocity profile(not a constant velocity).
 
gamz95 said:
Yes it is indeed frictionless. Therefore, when normal energy equation constructed the KE1=KE2(Since it says that velocities are the same). However, how is this physically possible? And question gives a changing velocity profile(not a constant velocity).
If you take the transient 1D momentum equation and integrate between the two ends of a control volume in which the velocity within the control volume is changing with time (and possibly position), you get the ordinary Bernoulli terms plus a term involving the rate of change of momentum with time within the control volume. See the PDF at Unsteady Bernoulli Equation - MIT OpenCourseWare that can be reached by googling transient Bernoulli equation.
 
  • Like
Likes   Reactions: gamz95

Similar threads

High School Why Do Objects Bounce? Exploring Momentum and Energy Conservation
  • · Replies 6 ·
Replies
6
Views
2K
High School Conservation of momentum and conservation of energy details
  • · Replies 30 ·
2
Replies
30
Views
3K
Undergrad Seemingly a contradiction of conservation of energy?
  • · Replies 51 ·
2
Replies
51
Views
5K
Undergrad Bernoulli's equation and the work energy theorem
  • · Replies 21 ·
Replies
21
Views
3K
Undergrad Conservation of Momentum versus Conservation of Velocity
  • · Replies 6 ·
Replies
6
Views
2K
High School Work Done By Conservative Forces
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Bernoull's Equation Derivation From Work - Energy Principle
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad What Explains the Paradox of Mechanical Energy Conservation?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Exit velocity through a nozzle: Bernoulli vs. Experience
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Bernoulli and Momentum Disconnect?
  • · Replies 4 ·
Replies
4
Views
2K