Dished head volume per product height calcs. 4

[GandLSimon]

Hello,

I have a BS 799 type B Horizontal cylindrical vessel with shallow type dished ends, I would like to know the volume of the product that the tank is holding at any given product level so that I can create a dip table. I have found some calculations for the cylindrical section but the heads are proving a bit tricky to grasp.

Can some body help with some calculations please.

If possible can we get together some calcs for the 2 different types of dished ends in the code.

i.e.
- Fig.3. Shallow dished end. Ri=1.5Do, Ri=>38mm (assume 40mm), Do=2700mm max.

-Fig.4. 6% Torispherical Dished end. Ri=Do. ri=6%Do

Assume tank is perfectly level.


If it helps the tanks dimensions are;
Do = 3099mm
Tan-Tan Length= 1970mm
Wall thk.= 6mm
Volume= 10000 L(Approx)


Many thanks in advance.
Simon

 

[Chance17]

See attached

 

[GandLSimon]

...Epic!

Many Thanks!

 

[JStephen]

Note also that you can numerically integrate head volumes using Simpson's rule, conveniently done via spreadsheet if the actual head geometry is known.

 

[unclesyd]

Here is paper by Bent Wiencke that covers the whole thing from end to end and some. On page 14 & 15 there are workable formats for all the information provided.

http://scanref.com/fileadmin/div_grafik/R_D/Computing_the_Partial_Volume_of_Pressure_Vessels.pdf