Volume of an Elbow Duct

Cross sectional area multiplied by length along the centreline must be a reasonable approximation for all practical purposes..

This begs the question why does it matter, what type of duct, what sort of accuracy are you after and what is your shoe size?

Del

See here!

It still smacks of huge overthink and looking for unnecessary accuracy.

If it's a rectangular duct, just measure half way across at regular intervals and mark dots, run a tape measure round the curve through all the dots and read off the length.

Multiply that by the cross sectional area of one end. Or if you want more accuracy. Measure the width to check if it is constant round the curve, it it's not, then measure at regular intervals and average it to give an average cross sectional area.

I can't see how the accuracy will be any less than some fancy formula that relies on you estimating a bend radius anyway.

Del

Yes. Usbport just did.

(Cross-sectional area) x (arc length of center-line radius). A local high-school geometry student could probably assist with this.

Where are all my Del's GAs you bunch of tightwads?

Kris

My crappy browser of the moment does not register GA or OT votes, nor does it have any text effects or link insertions in the reply window. The best I can offer is a rain check.

Curved pipes in the shape of circular arcs are frequently used in plumbing. To find the capacity of a pipe arc, you can consider the pipe as a section of a torus, and then use the formula for toric volume. When figuring volume of a curved pipe, you must know the outer diameter, thickness, band angle, and either the bend radius OR bend distance. See figure below:

Recall that if a torus has a diameter of X and a hole diameter of Y, then the equation for its volume is
Torus Volume = (π²/4)[(X/2)² - (Y/2)²](X/2 - Y/2)
For a torus sector with an angle measure of θ°, multiply the torus volume by a factor of θ/360. For example, if you have a 90° section of torus, the volume is multiplied by 90/360 or 1/4.
In the case of a curved pipe, we consider the interior of the pipe to be a torus section. If the pipe's width is c, the wall thickness w, and the bend radius r, then the torus diameter X and hole diameter Y are given by the equations
X = 2c - 2w + 2r, or
X/2 = c - w + r
Y = 2r + 2w, or
Y/2 = r + w
Putting all of the pieces together, you get the volume formula for a curved pipe:
Pipe Volume = (π²/4)((c-w+r)² - (r+w)²)(c-2w)(θ/360).

The volume by weighing method is probably accurate enough for most applications but that method requires you to have the elbow to seal it and weigh its contents. The above formulas allow you to make the calculations without having the elbow.

Good Luck, Old Salt

The source is: http://www.had2know.com/technology/curved-pipe-volume.html

Good Luck, Old Salt

Use a dB meter to measure volume.

There's a phart smone app for it.

1. Blank-off one end.
2. Fill it with water from a measuring cylinder filled to the top measuring line.
3. Once the elbow is full, observe the difference between a full measuring cylinder and the lower level after filling the elbow, and record it.