Calculating the Volume of a Duct Elbow

If the duct elbow makes a smooth turn, you can think of the curved part (excluding the straight ends which couple to the next sections of ductwork) as part of a torus, or donut. The volume of a torus can be computed by:

Volume = (1/4)π²(R + r)(R - r)²

where R is the outer radius of bend and r is the inner radius of bend.

This formula computes the volume of a complete torus. As the elbow does not make a complete 360° circle, the volume of the elbow will be some fraction of that. So, say your elbow makes a 45° bend. The actual volume of the bend will be 45/360 of the total volume computed above.

Does this help?

Thank you very helpful

Cab you tell me For the rectangular Duct Formulea

Thank you, its Great

Hi thank you so much for your information, but i'm confused with the "n" in the formula, Could you please tell me what the "n" stands for in the formula??

It isn't n, it's pi. The pi on the palette looks like an n. Can be confusing.

This should be fairly accurate:

For rectangular duct, you'll need to know (estimate) the bend radius. Typically measured from the "imaginary" centre of the bend arc to centre of the duct.

Look at profile of bend and ignore the width of the duct for the time being. Call the profile of the duct dimension L.

Radius R = bend radius + 1/2*L. Area A, use pi*R² to the outside of the bend.

radius r = bend radius - 1/2*L. Area a, use pi*r² to the inside of the bend.

Since an elbow is part of a circle (90 = 1/4 circle, 45 = 1/8 circle), you can calculate the area of a circle and divide by 4 (for 90) or 8 (for 45).

Area of cross section of 90 bend = (A-a)/4

For volume multiply this area by the (previously ignored) duct width.

For circular ducts, convert the cross sectional area of the duct to a square and use the same method as above. Square duct should have similar bend radius to your round duct.

Or you could ask RH

Europium has the most eloquent answer for round duct.

Check out

http://www.engineersedge.com/volume_calc/torus.htm

V=19.739Rr² (then divide by 4 or 8 for 90 or 45)

R=bend radius

r=1/2 of duct diameter

pressure decay on a duct? huh.