Hello Mechanical Engineers, I am 2

[refields]

Hello Mechanical Engineers,

I am working on a venting system and attempting to calculate head losses through the vent piping due to the friction of air flow. I don't have any issues with getting the Darcy Friction factor (using Churchill equations). My issue is that the Darcy-Weisbach equation is giving me head losses that are about 3 orders of magnitude too high compared to standard friction loss charts.

More than anything, I just want to understand how I am misusing/interpreting the Darcy-Weisbach equation. I've attached a spreadsheet which highlights the equation I am using (cell F35).

Thank you so much in advance!!

Reference friction loss chart:

https://www.engineeringtoolbox.com/ductwork-friction-loss-d_1122.html

 

[chicopee]

Are your calculations based on a 100ft long, smooth, galvanized, round duct? and about the fittings how are you addressing the pressure drop thru them?

 

[EnergyProfessional]

Assuming this is for a combustion appliance, why do you need to calculate that? the manufacturer gives vent sizing guidelines you need to meet regardless of your own calculations.

 

[refields]

Hi Chicopee, I have a 6" round cast iron duct (absolute roughness used is 0.00085 ft). The length is inclusive of the pipe runs and the fittings (equivalent fitting lengths from ASHRAE are used).

Hello EnergyProfessional, the application is that I need to ventilate a gravel layer below a building and so need to size a suction fan based on air change/head loss. I need to make the fan selection based on the head loss through the system.

I'm just trying to understand why the Darcy-Weisbach equation in the spreadsheet is giving such different results than the reference friction loss chart.

Thank you!

 

[EnergyProfessional]

I assume the pressure drop through the gravel layer will be dominant.
Check your calculation (units etc.)

 

[refields]

Hi, I believe the units used are correct (the units are itemized in the spreadsheet). I'm really stumped by this.

 

[BronYrAur]

Darcy-Weisbach is only for an incompressible fluid.

 

[quark]

The only problem is that you considered fluid properties of air and assuming pressure drop in liquid column. 1" air = 0.001293" water. 75.86*0.001293 = 0.098.

 

[chicopee]

So how much is the error between the spreadsheet and the Darcy-Weisbach equation.

 

[danschwind]

refields,

You can apply the Darcy-Weisbach equation to compressible fluids provided that the pressure doesn't drop wildly. If it does, you will need to split your system as the sum of several other systems with a lower pressure drop. Every time you start to calculate a new system, you will need to update your flow condition (density, velocity etc) based on the loss of your previous system.

 

[katmar]

I agree with quark. The form of the D-W equation that you have used gives the pressure drop as a head in terms of the flowing fluid. Since you have calculated the density of the air to be 0.0753 lbm/ft3 and the density of water is roughly 62.4 lbm/ft3, your answer is out by the ratio of these two densities, i.e. 828 times too large. The head in terms of water column would be 75.86 / 828 = 0.092 inches of water and this agrees with the other calculation.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[katmar]

Just a comment on the applicability of D-W to compressible fluids. The old rule of thumb was that if the pressure drop calculated by D-W was less than 10% of the upstream absolute pressure then the result was "accurate enough". In this case the pressure drop is 0.0033 psi and if the upstream absolute pressure is 14.7 psia then the pressure drop is only 0.022% of the upstream pressure and the answer should be OK. Switching my software between compressible and incompressible modes changes the answer in the fourth significant digit, so I would conclude that D-W is indeed "accurate enough" for this case.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[refields]

Quark, thank you!!!!!!!!!!! Katmar, thank you as well!!!!! Thanks to all that responded to my post. So obvious now. Ultimately I wanted to view pressures in terms of H2O though the calculation is for air flow and totally overlooked that this conversion was needed.

 

[BronYrAur]

Glad you were able to get that worked out.. As EnergyProfessional mentioned however, what about the pressure drop through the gravel? It seems to me that will be far greater than the ductwork.

 

[refields]

BronYrAur and EnergyProfessional,

This is a sub-slab depressurization system installed as part of a new building to mitigate vapor intrusion from VOC contaminants in the groundwater. Suction fans on the roof connect to vent risers that extend down into a 1' thick gravel layer below the slab on grade. The piping
then connects to pits laid out in the gravel layer as needed based on the foot print of the building.

Empirically, I know that as long as I can get about 4 inches of H2O vacuum at each extraction point, I'll have sufficient negative pressure at a radius of influence of about 50' to maintain a preferential pathway for VOC contaminants. We just need sufficient differential to overcome stack effects within the building that could life contaminants up through cracks in the slab on grade. The gravel used is roughly 3/4" diameter, poorly sorted, washed stone with a high void ratio and very little fines for high permeability.

I do not know how to actually calculate the pressure drop through the gravel. What we do is over-size the fan with a VFD. I have several monitoring points around the building perimeter (furthest points away from extraction points) where I can measure the vacuum in the gravel layer. Once it's installed and the fans turned on, we can reduce the frequency on the VFD if needed.

As I understand it, it would be very difficult to reliably solve for the pressure loss through gravel because of uncertainty with the boundary conditions (sub grade beyond the gravel).

thanks again

 

[EnergyProfessional]

Was the gravel selected with this mitigation method in mind? Most gravel also has many smaller particles to close the voids for better structural properties. that will have less conductivity for vapor however, when you want to extract gases, i assume you select gravel that allows more voids.


more voids means more fan power needed to maintain 4", but you also move more of the VOC. Fewer voids, less fanpower is needed, but you don't really move a lot of VOC. the duct here is the small problem and relatively known how to solve. the gravel is the big unknown. You may want to ask in a civil or environmental engineering forum for that.

 

[quark]

Usually, Ergun equation is used to check pressure drop across packed beds and liquids. You can check if that can help you. If the concern is about vapour migration above grade slab then the system you are considering a least resistance path. So, I don't see a bigger issue else I got it wrong.

 

[refields]

EnergyProfessional, we're using a washed high void ratio stone with very few fines. An example would by "AASHTO #57 stone"

http://capitolflexipave.com/wp-content/uploads/2012/08/AASHTO-57-Stone-Specs.pdf.

The structural engineers actually prefer this material below the slab on grade as it is self-compacting and drains very well. However, it is more expensive than other types of aggregate / fill.

 

[refields]

Quark, thank you for suggesting the Ergun equation, I will look into it further. I imagine the roughness and angularity of the aggregate are a significant factors and it would be interesting to see if such a calculation would be practical.