×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Are you an
Engineering professional?
Join Eng-Tips Forums!
• Talk With Other Members
• Be Notified Of Responses
• Keyword Search
Favorite Forums
• Automated Signatures
• Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

#### Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

(OP)
I need an equation for calculating the volume of a partially filled ASME F&D head on a vertical tank.  If anyone can help me out I would appreciate it.  Thanks in advance.

Chris

### RE: Partially filled head volume

I went through my reference books and even managed to dig out (after finding it) some old engineering documents I hoped might have it with no success.  Horizontal, yes.  Vertical, no.

However, the GPSA data book has a tabular set of data for the fractional volume of a vertical head at different liquid depths.  You might want to try curve fitting a set of data points depending on the accuracy you need.

### RE: Partially filled head volume

This is mostly about filling horizontal vessels, but prex' answer posted 22/10 includes a formula for filling the head of a vertical tank.

regards
Mogens

### RE: Partially filled head volume

(OP)
Thanks for the replies.  For anyone who may need similar information, I got the following formulas from Chicago Bridge & Iron Co bulletin #594, page 7:

Volume or contents of partially filled hemi-ellipsoidal heads with major axis vertical

Q= Partially filled volume or contents in ft^3
V= Total volume of one head in ft^3
R= Radius of cylinder in ft
delta= a/(KR) where
a= liquid height

It probably gives you the same result as the one refrenced above by mgp.

Unfortunately I was unable to find a formula for an ASME F&D head but I was able to fit a equation to curvature of tank in question.  Using this, I can find the volume of a solid of revolution bound between the curve and a horizontal line at the liquid level.  Kind of long but I think it will work close enough.

Once again thanks for effort TD2K and mgp.

Chris

### RE: Partially filled head volume

Check the reference
"Calculating Tank Volume" by Tim Broyles - Chemical Processing 2000 Fluid Flow Annual p.32
http://www.chemicalprocessing.com

### RE: Partially filled head volume

Gone are the days of everyone having the time to use second year university calculus and deriving the formulas from scratch by adding a couple of relatively simple integrals and solving for equation... I must be just too sentimental ...

### RE: Partially filled head volume

Hey Delta, I don't know if those days are gone, or not.  Last year I had to calculate the volume of a weir mounted up on the wall inside a vertical vessel.  The weir was open at the top and trapeziodally-shaped in section.  I had to calculate the volume (this was a skim trough in an IGF flotation cell) because the dump valve worked on a timer and we didn't want to blow a bunch of gas thru the dump valve and into the system.  So I set up a double integral, roated it thru 2pi, and it worked.  My old calc prof would have been proud.  I even did it in the field, in the control room, in the rain, during a startup!  How 'bout that!

Thanks!
Pete
P. J. (Pete) Chandler, PE
Principal Engineer
Mechanical, Piping, Thermal, Hydraulics
Processes Unlimited International, Inc.
Bakersfield, California USA
pjchandl@prou.com

Ahh, yes!

### RE: Partially filled head volume

The software cerebrotank give the exact parcial volume of vertical and horizontal tanks with any head commonly used.
Get a demo version in http://www.cerebromix.com.

#### Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

#### Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Close Box

# Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

• Talk To Other Members
• Notification Of Responses To Questions
• Favorite Forums One Click Access
• Keyword Search Of All Posts, And More...

Register now while it's still free!