Duct sizing using equal friction method

[mburns]

Using the Mcquay duct sizing formula i can simply put in the the amount of airflow (L/S) and the external static (pascals/pm) and it will spit out the velocity and equivalent round duct size.

e.g I only have to punch in.

Flow rate: 1000 (L/S)
Head Loss: 1 Pa/m

and it does the rest and it will come up with the answer
Velocity: 6.295 m/s
Round duct size: 449.7mm

Then i can work out equivalent duct sizes from there.

It's easy enough to punch some numbers in this program to get the answer but i wouldn't mind knowing the actual mathematical formula behind this calc. I've tried looking over the net for a specific formula but with no joy and read through a few text books but i'm not that clever at reverse engineering and transposing formulas.

[Yuri B.]

The pressure loss in pipes and tubes depends on the flow velocity, pipe or duct length, pipe or duct diameter, and a friction factor based on the roughness of the pipe or duct, and whether the flow us turbulent or laminar - the Reynolds Number (http://www.engineeringtoolbox.com/reynolds-number-d_237.html) of the flow. The pressure loss in a tube or duct due to friction, major loss, can be expressed as:

ploss = λ (l / dh) (ρ v2 / 2) (3)
where

ploss = pressure loss (Pa, N/m2)
λ = friction coefficient
l = length of duct or pipe (m)
dh = hydraulic diameter (http://www.engineeringtoolbox.com/hydraulic-equivalent-diameter-d_458.html) (m)
(3) is also called the D'Arcy-Weisbach Equation. (3) is valid for fully developed, steady, incompressible flow (http://www.engineeringtoolbox.com/entrance-length-flow-d_615.html).

This extract is from "Engineer toolbox". Air is not of course "incompressible", but for the speeds existing in air ducts it is said to be valid too. There should be hundreds good sources about duct calculation in the Internet, just use the searching engines like the Google.

[aramis]

Adding to Yuri B.'s post, you get the friction coefficient from the Moody diagram.

and you can check your calculations here:

http://www.engineeringtoolbox.com/darcy-weisbach-equation-d_646.html

[frank]

Here in the Uk we normally design to Velocity criteria, i.e. Low Velocity, Medium Velocity or High Velocity.

You have to decide which area you 'job' falls in.
Low Velocity - 0 - 5m/s
Medium Velocity - 5 - 10 m/s
High Velocity - 10+ m/s

You can size the duct using the formula V(ol) / A = V(el)

Transposing gives

A = V(ol) / V(el)
V(ol) = V(el) x A

[mburns]

Thankyou for the info guys. I understand you're way Frank (it's called velocity reduction i believe) and up until a few weeks ago i didn't even know there were other ways of sizing duct. Not that i do it, it's part of an engineering class i attend and i find it helps alot to know the formulas and calcualtions behind the software.

[Brian_UK]

In addition to the above information, if you want to read up on fans and ducts there is the excellent bible produced by Woods Fans, now Flakt, which can be downloaded in pdf format.

I haven't given a link as there are quite a few and you can search for it and perhaps get a nearer download site.
Search for "woods practical guide to fan engineering".

[mburns]

I've actually just found what i'm after. It's an actual design chart from an Airah ductork textbook. I'd looked at it before but couldn't understand it so i just left it, coming back to and giving a good read over it's what i'm after and it's quite easy to use. Basically choose you're desired pressure drop p/m of duct and you're airflow and you can find the velocity of the air and the size of duct you need.

As i said i'd use the software anyway but i find understanding things clicks into gear much better if i know how you get from A to B

[dougheret0]

Go to my web site www.nettally.com/doughert (http://www.nettally.com/doughert) and review the section on duct size with equal friction. You may download a free duct sizing ExCel program that will compute duct sizes and pressure losses for inputs of air flow and duct height (rectangular duct) or diameter (round duct). Remember that when you are laying out a duct system, the known values are the air flow in each branch and the space available for the ducts - often the height of a ceiling cavity. The program computes external static pressure for the supply and return critical duct paths.

The web site includes the article that appeared in the May 2009 ASHRAE journal describing the formulas and the VBasic code used to develope the program. In IP units.