mrev23
Mechanical
- Mar 20, 2014
- 26
thread403-435647
My conclusion after reading the referenced thread, etc.:
For a bell mouth inlet on a rectangular duct in a return air plenum: using a 6” bell length with 45-degree sides is probably adequate – if it can fit in the available space.
Some TL;DR for that conclusion:
As said in the first post by LittleInch: ”Depends on what you want the average inlet velocity to be.”
I most often see bell mouth inlets (as opposed to bell mouth duct takeoffs) in return air plenum applications. In these cases, one may simply want “less” pressure drop than would exist through an open-ended duct.
As noted in the second post by LittleInch a size ratio of 2:1 results in a velocity ratio of 4:1 – which (because dynamic losses are proportional to the square of the velocity) leads to a pressure drop ratio of 16:1 – a 94% reduction in pressure drop. For a return air plenum application, this would be far beyond achieving “less” pressure drop than would exist through an open-ended duct.
If it will fit in the available space, the file linked by Capliard suggests, in a roundabout way, that a good starting point is for the inlet of the bell to be at least twice the duct area – not twice the duct size.
The illustration in the link by Capliard shows a bell with constant radius of not less than 0.2 times the duct diameter for a round duct.
For r = 0.2 * D, the inlet area is nearly twice the duct area. To achieve an area ratio of 2:1, the radius of the bell would be r = (sqrt(2) - 1) / 2 * D, which is ~ 0.21 * D.
The same formula works for a square duct if the “bell” has flat (instead of radiused) sides at 45-degrees to the axis of the duct.
With the resulting 2:1 area ratio, the pressure drop ratio would be 4:1. A 75% reduction in the pressure drop (neglecting the presence of a screen on the inlet of the bell mouth) probably exceeds the designer’s desire for “less” pressure drop than would exist through an open-ended duct.
For a rectangular duct with a “bell” whose flat sides are at and angle of 45-degress to the axis:
L = (–2*H*(AR + 1) + sqrt((2*H*(AR + 1))^2 – 4 * 4 * (AR * H^2 * (1 – K))) )/ 8
Where:
• L= the length of the bell, measured along the axis of the duct -- and (because it is a 45-degree bell) -- = the distance from the side of the duct to the edge of the bell
• H = Duct height
• AR = Aspect ratio = duct_width / duct_height
• K = Area ratio = area_of_bell_inlet / area_of_duct
The above is from solving this for L:
K = (AR * H + 2*L) * (H + 2*L) / AR * H^2 -- which uses AR * H = W = duct_width
A detail for a bell mouth inlet may need to describe how the edges of the bell are to be reinforced.
Though the length of a bell with an area ratio of 2:1 may be less than 6” in many cases, it may not be worth the effort to determine what that length would be.
Likewise: for large ducts, a bell length might need to be longer than 6” to achieve an area ratio of 2:1. But how critical is it to slow down the air by a factor of 2 in this application? And, as noted by LittleInch: “the velocity across the end area won't be uniform”. So what is to be gained by making the bell 8” long instead of 6” long in a ceiling plenum, where space is usually at a premium?
Though (to my knowledge) Nordfab is not in the comfort HVAC business, the best table I found to show the dimensions of round bell mouth inlets is here:
This table is based on values found there:
[pre]
DD BD L L/DD BD/DD Area_ratio
3 6 4.5 1.5 2 4
4 7 4.5 1.13 1.75 3.06
5 8 4.5 0.9 1.6 2.56
6 9.5 5 0.83 1.58 2.51
7 10.5 5 0.71 1.5 2.25
8 11.5 5 0.63 1.44 2.07
9 12.5 5 0.56 1.39 1.93
10 13.5 6 0.6 1.35 1.82
11 16.5 6 0.55 1.5 2.25
12 17.5 6 0.5 1.46 2.13
13 18.5 6 0.46 1.42 2.03
14 19.5 6 0.43 1.39 1.94
15 20 6 0.4 1.33 1.78
16 23 7 0.44 1.44 2.07
17 24 7 0.41 1.41 1.99
18 25 7 0.39 1.39 1.93
19 26 7 0.37 1.37 1.87
20 27 7 0.35 1.35 1.82
21 27.5 8 0.38 1.31 1.71
22 30.5 8 0.36 1.39 1.92
23 31.5 8 0.35 1.37 1.88
24 32.5 8 0.33 1.35 1.83
[/pre]
DD = duct diameter, BD = bell inlet diameter (inside the flat portion), L=length of the bell
They seem to be trying to approach an area ratio of 2, where practical.
There are also elliptical bell mouths, as noted in the post below. But I can’t imagine that it is necessary in most HVAC applications.
The post with the image of the elliptical profile is followed by a lament, “This is the third 'Standard' I have seen in as many weeks.”
It rhymes with this from Andrew Tanenbaum: “The good thing about standards is that there are so many to choose from.”
As for sizing a bell mouth inlet in general, what LittleInch said: ”Depends on what you want the average inlet velocity to be.”
My conclusion after reading the referenced thread, etc.:
For a bell mouth inlet on a rectangular duct in a return air plenum: using a 6” bell length with 45-degree sides is probably adequate – if it can fit in the available space.
Some TL;DR for that conclusion:
As said in the first post by LittleInch: ”Depends on what you want the average inlet velocity to be.”
I most often see bell mouth inlets (as opposed to bell mouth duct takeoffs) in return air plenum applications. In these cases, one may simply want “less” pressure drop than would exist through an open-ended duct.
As noted in the second post by LittleInch a size ratio of 2:1 results in a velocity ratio of 4:1 – which (because dynamic losses are proportional to the square of the velocity) leads to a pressure drop ratio of 16:1 – a 94% reduction in pressure drop. For a return air plenum application, this would be far beyond achieving “less” pressure drop than would exist through an open-ended duct.
If it will fit in the available space, the file linked by Capliard suggests, in a roundabout way, that a good starting point is for the inlet of the bell to be at least twice the duct area – not twice the duct size.
The illustration in the link by Capliard shows a bell with constant radius of not less than 0.2 times the duct diameter for a round duct.
For r = 0.2 * D, the inlet area is nearly twice the duct area. To achieve an area ratio of 2:1, the radius of the bell would be r = (sqrt(2) - 1) / 2 * D, which is ~ 0.21 * D.
The same formula works for a square duct if the “bell” has flat (instead of radiused) sides at 45-degrees to the axis of the duct.
With the resulting 2:1 area ratio, the pressure drop ratio would be 4:1. A 75% reduction in the pressure drop (neglecting the presence of a screen on the inlet of the bell mouth) probably exceeds the designer’s desire for “less” pressure drop than would exist through an open-ended duct.
For a rectangular duct with a “bell” whose flat sides are at and angle of 45-degress to the axis:
L = (–2*H*(AR + 1) + sqrt((2*H*(AR + 1))^2 – 4 * 4 * (AR * H^2 * (1 – K))) )/ 8
Where:
• L= the length of the bell, measured along the axis of the duct -- and (because it is a 45-degree bell) -- = the distance from the side of the duct to the edge of the bell
• H = Duct height
• AR = Aspect ratio = duct_width / duct_height
• K = Area ratio = area_of_bell_inlet / area_of_duct
The above is from solving this for L:
K = (AR * H + 2*L) * (H + 2*L) / AR * H^2 -- which uses AR * H = W = duct_width
A detail for a bell mouth inlet may need to describe how the edges of the bell are to be reinforced.
Though the length of a bell with an area ratio of 2:1 may be less than 6” in many cases, it may not be worth the effort to determine what that length would be.
Likewise: for large ducts, a bell length might need to be longer than 6” to achieve an area ratio of 2:1. But how critical is it to slow down the air by a factor of 2 in this application? And, as noted by LittleInch: “the velocity across the end area won't be uniform”. So what is to be gained by making the bell 8” long instead of 6” long in a ceiling plenum, where space is usually at a premium?
Though (to my knowledge) Nordfab is not in the comfort HVAC business, the best table I found to show the dimensions of round bell mouth inlets is here:
This table is based on values found there:
[pre]
DD BD L L/DD BD/DD Area_ratio
3 6 4.5 1.5 2 4
4 7 4.5 1.13 1.75 3.06
5 8 4.5 0.9 1.6 2.56
6 9.5 5 0.83 1.58 2.51
7 10.5 5 0.71 1.5 2.25
8 11.5 5 0.63 1.44 2.07
9 12.5 5 0.56 1.39 1.93
10 13.5 6 0.6 1.35 1.82
11 16.5 6 0.55 1.5 2.25
12 17.5 6 0.5 1.46 2.13
13 18.5 6 0.46 1.42 2.03
14 19.5 6 0.43 1.39 1.94
15 20 6 0.4 1.33 1.78
16 23 7 0.44 1.44 2.07
17 24 7 0.41 1.41 1.99
18 25 7 0.39 1.39 1.93
19 26 7 0.37 1.37 1.87
20 27 7 0.35 1.35 1.82
21 27.5 8 0.38 1.31 1.71
22 30.5 8 0.36 1.39 1.92
23 31.5 8 0.35 1.37 1.88
24 32.5 8 0.33 1.35 1.83
[/pre]
DD = duct diameter, BD = bell inlet diameter (inside the flat portion), L=length of the bell
They seem to be trying to approach an area ratio of 2, where practical.
There are also elliptical bell mouths, as noted in the post below. But I can’t imagine that it is necessary in most HVAC applications.
The post with the image of the elliptical profile is followed by a lament, “This is the third 'Standard' I have seen in as many weeks.”
It rhymes with this from Andrew Tanenbaum: “The good thing about standards is that there are so many to choose from.”
As for sizing a bell mouth inlet in general, what LittleInch said: ”Depends on what you want the average inlet velocity to be.”