Flow through a branch

[Engineer6512]

This should be a fairly simple problem, but I am not sure if I have enough information to solve it.

I have a 12" diameter circular duct, 60 feet long. I have a static pressure of 25" W.G. at the inlet. This duct is discharging into another duct having a static pressure of 18" W.G. I need to calculate the airflow through this portion of duct. Is this enough information to solve this?

 

[quark]

To some extent. In the absence of pressure dropping devices like dampers and filters etc., main pressure drop comes from the friction. Use Darcy's formula to calculate velocity as you already know the pressure drop, equivalent diameter and length of the duct.

 

[Engineer6512]

Thanks for the reply. I think I understand what you are saying, but I just need some clarification:

In this case the SP drop is not due completely to friction. The duct system that this duct is discharging into has its own lower SP. It is the differential SP that is driving this flow. Does this make sense?

 

[quark]

What you should account for is (25-18)= 7" of wc which is disappearing in the branch.

 

[katmar]

What you say does make sense, and there is enough info to make a rough estimate.

If the source and destination are held at 25" and 18" respectively, the flowrate of the air will increase until the full 7" differential is made up by the friction head.

As an analogy, think of putting a shunt resistor directly across the terminals of a battery. The current through the resistor increases until the voltage drop across the resistor is equal to the voltage of the battery.

With such a big pipe, you will get a large flowrate - approx 6000 scfm (depending on the temperature and the fine detail of the pipe geometry). This is a velocity of about 125 ft/s. Can your source deliver this rate and maintain 25" WG? Can the destination accept this flowrate without increasing its pressure? Those are the practical questions to answer.

 

[friartuck]

Beazley

You need to do a repetitive/reiterative calculation. I would start at assuming the pressure of 7" wg is all velocity pressure (which it wont be,but its a starting point)

transpose VP= 1/2 x rho x V squared

so Vel= sqrt of 2 x VP/Rho

use 7x250 = Pascals
Rho for air is about 1.2kg/m3

so vel is 54m/sec (a bit quick)

With this velocity, estimate the duct PD using normal methods (i.e.duct charts and so on)

You will find that the duct PD is over 7" WG, so gradually drop the velocity until you match the PD to your 7" wg.


You will need a few charts or failing that some fancy equations

Darcy 4fLV2/2GD (four x Fx V squared divided by 2 x G x Dia)for duct PD (or colebrooke and white if you have an hour or two to work it out)


good luck





Friar Tuck of Sherwood

 

[quark]

I agree with Katmar. The flow can be around 6113cfm with a velocity of 7783fpm(All the iteration is done by McQuay's DuctSizer.

Note that this is the maximum flowrate you can squeeze through the 12" duct with a frictional drop of 7". Actually, this will be low due to the losses at entry and exit.

What is the application?

Regards,

 

[katmar]

Hi quark,

Thanks for the reference to McQuay's DuctSizer. I am not an HVAC person and I was not aware of this very useful tool. I downloaded it as I am always keen to test other tools against my own software. I ran a few examples and what I found was that although you and I came to the same answer, it was a coincindence and we were both wrong.

In my calculation I had assumed that the velocity head would be lost. This is wrong because it is discharging into an 18" WC system and the velocity head (velocity pressure in McQuay-speak) would be recovered. This means all 7" of available head can be used to overcome the pipe friction.

In your calculation you appear to have set the head loss to 7" per 100 ft, but Beazley's duct is only 60 ft long. When I set my software to allow recovery of velocity head and I set the pressure drop in DuctSizer to 11.667 inWC/100 ft then I get the same answer with both tools. The flowrate is now 7900 cfm. It seems that DuctSizer does not have an option to disallow velocity head recovery.

As you pointed out we have neglected entrance and fitting effects, so the actual flowrate would be a bit less than this.

DuctSizer does not have an input for pipe roughness. By trial and error in my software I adjusted the roughness until I got the same friction factor as DuctSizer. This occurs at a roughness of 0.00843 inch (0.214 mm) which seems like a perfectly reasonable (slightly conservative) number to me.

This exercise emphasizes the need for calcs to be checked. Years ago I had an engineer complain to me that he felt insulted because our company policy was for all calcs to be checked by a second engineer. I explained to him that it is an engineer's right to insist that his calculation be checked because society holds us engineers responsible for our work and the engineer is entitled to expect the company to protect him. Once he saw it from this point of view he was always happy to have his calcs checked, and I always like to have my calcs at least reviewed by someone I trust.

Anyway, I was happy to see DuctSizer confirm my software's results. Perhaps software also has the right to an independent check!

 

[Engineer6512]

Thanks for the replies guys. It was a great help.

 

[quark]

This exercise emphasizes the need for calcs to be checked. Years ago I had an engineer complain to me that he felt insulted because our company policy was for all calcs to be checked by a second engineer.

True and when the problem happens we tend to say that 'there is something wrong terribly otherwise we shouldn't have done that silly mistake'.

You are correct that I mistook the pressure drop of 7" for 100ft. This is not a cover but I did think of the 60ft but didn't put it in the software(there is something.....).

That is hell lot of a velocity for a 12" duct and I feel like I am hearing the noise and experiencing the vibration. I wish the OP would through some light on the practical aspects of this situation.

Regards,