8 replies to this topic

[Sherif Morsi]

Hi,

 

I am doing some calculations regarding the release rate of liquids from a leak (small hole) in a spherical tank. I am trying to compute an equation for the partial volume (i.e. when the tank is partially filled with liquid).

 

Help is appreciated

 

Sherif

[Lucian Gomoescu]

Hello Sherif,

Attached you find all you need to relate liquid level with volume in case of a spherical tank.

I presented the equations for finding volume V when level L is known. For vice versa problem, you can use an Excel goal seek (adjust level until volume is equal to known V).

Enjoy,
Lucian

Attached Files

•  Spherical Tank.jpg   48.79KB   22 downloads

[Bobby Strain]

One formula should do it, with level from the bottom to full. Two are unnecessary. Try it.

 

Bobby

[breizh]

Hi Sherif ,

Bobby is right , consider the link attached to support your work .

 

http://www.1728.org/diamform.htm

 

Breizh

[samayaraj]

Partial volume of sphere = pi()*h^2*(1.5d-h)/3

Where as h is height of liq from bottom of tank, d is the inner dia of tank...

[Bobby Strain]

Would one of you scholars care to lead us through the derivation of this formula? I have gone through the formula for a cylinder partial volume, which is quite easy and straightforward. I guess if I take the time I may be able to do the same for a sphere. But I am much slower now, so I rely on code.

 

Just a note; if you find you want to know various geometry of a cylinder you can find same at my website. And, for a sphere, you can choose spherical heads with a 0 length cylinder. The various dimensions are calculated through a library, easy to access, and cannot be easily tampered with. You can do the same and still use your favorite spreadsheet tools. Don't stop learning when you master spreadsheet formulas. They are nasty to deal with, impossible to validate, and unrecoganizable after 2 months.

 

Bobby

Edited by Bobby Strain, 12 December 2015 - 10:31 PM.

[samayaraj]

Hi,

 

Find attached the excel sheet to calc partial vol of spherical tank. You can also check the result from Vessel Volume calculator in the below link by selecting horizontal tank with T/T distance as Zero and head as hemispherical head. The result will be partial vol of spherical tank.

 

http://www.cheresour...al-volume-tool/

Attached Files

•  Partial vol of spherical tank.xlsx   10.66KB   58 downloads

Edited by samayaraj, 13 December 2015 - 12:42 PM.

[Ajay S. Satpute]

Would one of you scholars care to lead us through the derivation of this formula? I have gone through the formula for a cylinder partial volume, which is quite easy and straightforward. I guess if I take the time I may be able to do the same for a sphere. But I am much slower now, so I rely on code.

Bobby

 
Hi Bobby,
 
You may refer below link.
https://www.physicsf...-sphere.211433/
 
Regards.
 
Ajay

[Lucian Gomoescu]

Hello Bobby,

Attached you can find the derivation of partially filled sphere. I made it short and without much words because of the figure, which is enough to understand the notations.
 

You and the others were right that one formula is enough for entire range of level. In the first post i split the domain in two because i found nowhere a simple mention that the formula applies for 0 <= H <= 2R.
 

 

Best regards,
Lucian

Attached Files

•  Spherical Tank Partial Vol - formula derivation.pptx   62.91KB   38 downloads