Change in pressure when merging tubes

[Gerald Funk]

Homework Statement

hello, I have a problem that I couldn't find a clear answer to. Attached is a diagram of a related problem that explains the problem

Air traveling through two tubes with the same direction have the same PSI (say 75). If you merge the two tubes into a tube with the same diameter as the previous two, what happens to the pressure of the moving air? Does it double?

Homework Equations

The Attempt at a Solution

I think the pressure would double, but I am unsure

 

[gneill]

Have you investigated the Bernoulli equation for this setup? If the tube diameters are all the same, how are the velocities of the air in each section related?

 

[Gerald Funk]

I don't know if the original problem is that complicated. Let's say the source of air is two identical air compressors set to the same settings, so the PSI, the velocities, and the volume is the exact same for both tubes.

 

[gneill]

Apply Bernoulli. Really

You'll have to put a small bit of thought into deducing the velocity in the merged tube. Assume that the tubes are lying on the ground (you're looking down on them) so there's no change in height involved.

 

[Gerald Funk]

I am still having troubles getting my head around this. The problem is that any time I've used the Bernoulli equation, its only looking at one tube (like a Laval nozzle where one tube gets smaller), but this question has two tubes feeding into one. So this equation:

would need a p3 and v3 somewhere in there, but I can't figure out how to integrate it

 

[gneill]

You said that the pressure and flow rate in the feeds were identical. Thus each feed moves the same volume of air into the exit tube per unit time. Knowing the dimensions of the tubes, that should allow you to determine what the flow rate (hence velocity) must be in the exit tube. A flow streamline can be chosen in one feed tube and followed to the exit tube. We assume no turbulence, hence laminar flow. Apply Bernoulli to that streamline. Two velocities, two pressures. You know the two velocities and one of the pressures...