Bernoulli vs Energy Conservation?

AI Thread Summary
The discussion revolves around the relationship between Bernoulli's principle and energy conservation in fluid dynamics, specifically questioning the implications of having the same velocities at both ends of a tube. Participants highlight that identical velocities do not necessarily indicate no energy loss, especially in the presence of turbulence. The problem states a "frictionless flow," leading to the conclusion that kinetic energy at both ends can be equal, but this raises questions about the physical feasibility given a changing velocity profile. The integration of the transient 1D momentum equation reveals that additional terms must be considered, which include the rate of change of momentum. Overall, the conversation emphasizes the complexities of applying Bernoulli's equation in dynamic scenarios.
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In the example, is it possible to have same velocities at the two ends of the tube? How would you construct energy conversation equation?
 
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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."
 
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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.
 
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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.
 
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