# Are there equations for figuring out inner and outer radii of reducing bends?

• dughug
In summary: It actually works, even though I said it didn't in my last reply. Just make sure you draw your lines long enough when you fillet it in Autocad. Use those equations, you can make it work, absolutely.
dughug
Hi folks. I work as an AutoCAD drafter for a wastewater/water engineering company. I use a manual, the American Pipe Manual to help me draw different types of pipe fittings. When I come to the 90 degree reducing bends, the only information I get is the center radius of the bend. Example: 6"x 4", 90 degree reducing bend has a center radius of 6". But the manual does not give inner and outer radii. So my question is, how do pipe engineers figure out what the radii will be for the inner and outer radii before the casting process. Are there equations to figure out the inner and outer radii, if only given information of the center radius? I'll attach a *.bmp file so you can see an example of what I'm trying to draw.

#### Attachments

• bend_radii5.bmp
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Hello. Do you actually need the radii? The two yellow quarter circles appear to be normal to the horizontal and vertical planes. In Solidworks, I would just create points on both sides of the center curve at its ends, and connect those points with a quarter arc. The software would then provide me the metrics (length, radius, center, etc.).

ThalorB said:
Hello. Do you actually need the radii? The two yellow quarter circles appear to be normal to the horizontal and vertical planes. In Solidworks, I would just create points on both sides of the center curve at its ends, and connect those points with a quarter arc. The software would then provide me the metrics (length, radius, center, etc.).

Thanks for your reply ThalorB. I don't know Solidworks, so I can't picture what you are trying to explain. In AutoCAD I use a command called offset, but in this case you can't offset the radius because one end of the bend is larger/smaller than the other. Its just something that has been really bugging me. I'm just wondering what Pipe engineers used, if any calculations to create these reducing bends. Anyone?

Sure there is:
$$s=r \theta$$

where
s = arc length
r = radius
$$\theta$$ = angle of arc in radians.

You will need a way to measure the arc length of the inner and outer radii to calculate the radius after using the offset command. I can't remember if the properties of the arcs will give that to you or not. It has been a while. IIRC, I had a small lisp program that gave me arc lengths.

FredGarvin said:
Sure there is:
$$s=r \theta$$

where
s = arc length
r = radius
$$\theta$$ = angle of arc in radians.

You will need a way to measure the arc length of the inner and outer radii to calculate the radius after using the offset command. I can't remember if the properties of the arcs will give that to you or not. It has been a while. IIRC, I had a small lisp program that gave me arc lengths.

Thanks for the reply Fred. Ok, I tried the inner radius. Here's the numbers.

The properties box of the polyline(rather than actual arc) gave me:

s = 10.2832 inches
r = 90 degrees, converted to radians = 1.5707963268
$$\theta$$ = 6.5464884 radius

When I tried to use the "fillet" command for the 6.546 radius value, I get the error: radius is too large. Any suggestions? Doing anything wrong?

I tried it on my computer and it worked fine for two perpendicular lines and a polyline. I guess the first thing I would ask is are your line lengths long enough to accommodate that large of a radius?

FredGarvin said:
I tried it on my computer and it worked fine for two perpendicular lines and a polyline. I guess the first thing I would ask is are your line lengths long enough to accommodate that large of a radius?

That's what I did, was extend the line lengths, and it works fine now. Thanks so much!

how did you draw the arcs for the inner and outer radii? I'm trying to figure out how to do this as i have an interview with a boiler parts maker coming up.

warz2013 said:
how did you draw the arcs for the inner and outer radii? I'm trying to figure out how to do this as i have an interview with a boiler parts maker coming up.

It actually works, even though I said it didn't in my last reply. Just make sure you draw your lines long enough when you fillet it in Autocad. Use those equations, you can make it work, absolutely. If you have any other specific questions, ask away, I'll try to help. -Doug

## 1. What are reducing bends and why are they important in engineering?

Reducing bends are curved sections of a pipe or tube that gradually decrease in diameter. They are important in engineering because they allow for changes in the flow of fluids or gases, and can also be used to connect pipes of different sizes.

## 2. Is there a specific equation for calculating the inner and outer radii of reducing bends?

Yes, the most commonly used equation for calculating the inner and outer radii of reducing bends is the D’Arcy-Weisbach equation. This equation takes into account the fluid flow rate, fluid density, pipe diameter, and friction factor to determine the radii.

## 3. How do I determine the ideal inner and outer radii for a reducing bend in a specific application?

The ideal radii for a reducing bend will depend on the specific application and the design requirements. Factors to consider include the flow rate, fluid properties, pressure drop, and space limitations. Consulting with a mechanical engineer or using simulation software can help determine the most efficient radii for a given application.

## 4. Can I use the same equation for all types of reducing bends?

The D’Arcy-Weisbach equation can be used for most types of reducing bends, including standard 90-degree bends and more complex bends with varying angles. However, for specialized bends, there may be other equations or methods that are more appropriate.

## 5. Are there any other factors that need to be considered when calculating the inner and outer radii of reducing bends?

In addition to the parameters included in the D’Arcy-Weisbach equation, other factors such as the material and thickness of the pipe, as well as the support and reinforcement of the bend, should also be taken into account. These can affect the strength and stability of the bend and should be considered in the design process.

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