Parallel flow in duct - general question

[planetp]

Please forgive me for the Engineering 101 question that I'm about to ask.

I'm having problems visualizing pressure drop in parallel flow. Refer to the JPEG attached for this example.

http://files.engineering.com/downlo...bc0828f265a&file=ParallelFlowPressureDrop.jpg

In this particular example I have a smooth duct, 20 mm high by 60 mm wide by 1 m long. There is air flow through the duct at 4 m/s and after determining the hydraulic diameter and Reynolds number, I calculate the pressure drop through that length of duct as being 10.4 Pa.

Now I add two infinitely thin walls in the duct that split the flow equally into 3 channels 20 mm wide. The velocity hasn't changed because the walls are thin. I calculate the pressure drop of each of the 3 channels as 17.5 Pa. When I take the inverse sum of the inverses (parallel flow), I have a total pressure drop of 5.8 Pa.

I'm having difficulty trying to get a practical sense of what is going on here. How is the pressure drop going down just by adding baffles. It seems like the reverse should happen, since I'm adding frictional flow resistance.

Is my assumption of equal velocity between the duct with no baffles wrong? If so, how do I calculate the true velocity in the smaller channels?

 

[rbcoulter]

Your flaw is that Pressure drop in parallel is not computed by reciprocal of reciprocal sum relationship. That is for the resistances the channels, not the pressure drop. The pressure drop is the value you calculated for each small channel.

 

[planetp]

OK, makes sense. Pressure drop similar to voltage drop.

So would the process for determining overall pressure drop (across all three channels, which may or may not be equally sized) to determine the actual velocity in each channel that would result in the same pressure drop across each channel? Maybe solve this by matrix algebra?

 

[rbcoulter]

Yes. It's similar to electrical circuits. Voltage drop is like pressure drop - they are measure from node to node.
If the channels were different sizes then the flows in each channel would vary to make the pressure drop the same in each path (assuming they all share the same nodes). Iterative algorithms are often needed depending on the flow resistance equations.

 

[davefitz]

If the 3 channels had different geometries or other characteristic differences, then one would calclulate the flow vs DP curve for each of the 3 channels, then for each assumed DP,add the 3 flows to generate a common DP vs total flow curve.

The boundary condition that is common to all 3 channels is they operate with the same overall DP.

If the total flow is known beforemhand, then determining the DP is simple. If the total flow is not known and you know instead the pump or fan characteistic curve, then the intersection of these 2 curves yields the operating point of flow and DP.