Pipe pressure drop calculation

[charlyliz]

I am calculating various pressure drops in a pipe and am and am having trouble calculating the pressure at a certain point, for a set case. This is the pipe...

http://i50.tinypic.com/141mikg.jpg

A and B are vents, through which air passes and travels on up the pipe, where is it discharged to atmosphere. I am working out the pressure at points a and b for three cases.

1) both vents open and pumping air
2) vent A open, vent B closed
3) vent A closed, vent B open

I have worked everything out no bother for cases 1 and 2 but 3 is stumping me. My engineering brain knows that there should be a vacuum effect at a, because of the flow through b onwards, but I can't work out how to do the calculation. So far, setting the flow rate at a to zero just makes the frictional losses zero at this point, and leaving it at the same pressure as at b ... which isn't right!

I have accounted for losses due to the fittings (inlets) in my calculation.

I would like to know a method to calculate pressure at a when vent A is closed.

Thanks in advance.

 

[Valkarie]

The method for calculating the pressure at point a with vent A closed is to use the Bernoulli equation. The Bernoulli equation states that the sum of the pressure, kinetic energy, and potential energy is constant along a streamline. In this case, you can assume that the velocity is zero at point A (since vent A is closed) and the potential energy is also zero since this is a steady-state flow. Therefore, the pressure at point A will be equal to the pressure at point B, since the sum of all energies must remain the same.