138 posts

### Re: Material in Dome Calculation

fact09,

You could simply register to photobucket or a similar (free) image hosting site.

There you can upload your picture and re-use the url pointing to your picture.

For example:

**La diseuse de bonne aventure (Le Caravage)**

It is very unfortunate that cemnet doesn't offer image hosting for posters.

This is an obstacle for good communication, but there can be reasons to do so.

**Know the answer to this question? Join the community and register for a free guest account to post a reply.**

10 posts

### Re: Material in Dome Calculation

Lalbatros and fellow contributors to the Technical Forum,

After reading your posts, I have found a way for you to upload images/documents to the technical forum. When creating a new post or replying to an existing one, you should see an 'options' tab above - click it and then click 'add/update' button underneath the File Attachments section. From there a very user unfriendly window will open which you will have to manually expand, but it will enable you to upload.

I’ll get this improved shortly, but for the mean time please bear with it.

I’m sure you don’t need reminding but please virus scan anything you download from a public forum!

Best regards

CemNet Forum Administrator

16 posts

### Re: Material in Dome Calculation

Forum Administrator,

After many attempts I was finally able to upload the image. The reason why it was not letting me upload images was because the file was over 1 Mb. After I got it to about 40kB then your upload option worked.

Lalbatros,

Something I forgot to include in the drawing is the following:

Dome Volume (V1) = pi * rc * h^2 - .33 * pi * h^3 |

where, |

rc=( h^2+r1^2)/2h Regards, |

138 posts

### Re: Material in Dome Calculation

fac09,

The picture below should answer your original question.

However, I am not sure I did understand your geometry correctly, please check.

I assumed you are interrested in the volume of an hemisphere having a cone removed from it, as in the picture below.

I guessed from your drawings that you would like to take into account the additional effect of this volume being packed down, not touching completely the dome. If this is right, you should simply take that into account by applying an additional factor on the result (see below last formula).

In the lower right, I give the formula for the volume of deep-yellow part of the dome.

This formula is rather easy to prove:

The volume of an hemisphere is:

Vo = 2/3 Pi R³

The surface of an hemisphere is:

So = 2 Pi R²

The surface of the dome cap that is empty of material is:

S1 = 2 Pi R² (1-sin(q))

Therefore the volume removed from the dome is:

V1 = S1 / So Vo = 2/3 Pi R³ (1-sin(q))

Therefore the volume of the dome filled with material is

Vdome = Vo - V1 = 2/3 Pi R³ sin(q)

To take an additonal "packing down effect" would give the volume of material:

Vmaterial = Vdome * h(actual) / h(maximum)

The formula for the dome cap can be found in many formularies or can easily be calculated by integration.

Michel