Mass loss in Bernoulli's Principle?

[udtsith12]

Hi, I could really use help. I am trying to understand what would happen to the velocity of a freestream air if it loses mass while traveling down a tube. For example, suppose that you have 1 cubic meter of air traveling at 10 m/s down a duct with a 1m^2 cross section. And then suppose that you lose via pumps along the tube 90% of the air. Or another way to say it... suppose that 90% of the air just disappeared as it was traveling down the pipe. What would be the resulting velocity of the remaining air? My closest guess is that it would be reduced to 1 m/s. Is that right? Thanks!

 

[cjl]

Assuming that your flow is slow enough to consider incompressible, then yes, simple continuity would indicate that it would slow down to 1m/s. This isn't due to Bernoulli, it's just the continuity principle.

 

[Lnewqban]

Welcome, udtsith12

If you observe a duct system for ventilation or air conditioning, you could see that the area of the cross-section is reduced (for supply ducts) or increased (for return ducts) gradually as the flow advances downstream, more or less after one or two air diffusers or grilles.

Those changes of cross-section have the purposse of avoiding as much as possible changes of the velocity of the airstream as it loses mass while traveling down the duct.