Bernoulli vs Energy Conservation?

[gamz95]

In the example, is it possible to have same velocities at the two ends of the tube? How would you construct energy conversation equation?

 

[sophiecentaur]

Why would you expect mechanical energy to be conserved if there is any turbulence involved? Same velocities doesn't imply no energy loss.

 

[Chestermiller]

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."

 

[Chestermiller]

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.

 

[gamz95]

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).

 

[Chestermiller]

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.