# Volume of a tank

L

#### LUZ GARCIA

Does anyone knows how to calculate the volume of fluid of a round tank with a fluid measured 2 ft below the full mark?

Also what about the expected change in volume for an increase of 10 degrees Fareinheit if the fluid is gasoline?

What would be the change in volume of both fluids if a tank contains 500 gallons of water and 9,500 gallons of gasoline with the same temperature change?

Thanks LF

A

#### Art Bourdeau

Look at CRC Standard Math Tables. I am looking at the 20th edition, pg. 17.
V= 1/3 (pi) h^2(3R-h)
V=volume
h= distance from top to surface - part not filled - air space.
R= radius of sphere
Expansion rate of gasoline would be in the chemistry part.
Regards,
Art Bourdeau,
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#### Bruce

Is that "round" as in spherical, or "round as in horizontal cylinder?

For a sphere, Perry gives

V = 1/6 PI h1 (3 * r2^2 + h1^2)

where PI = 3.1415926....
h1 is the vertical height to the surface
r2 is the horizontal radius of the surface.

For a horizontal cylinder, the volume is

V = L * r^2*arccos(r-H)/r - (r-H)sqrt(2rH-H^2)

where L = length of cylinder
r is radius of cylinder
H is vertical height of surface from the top

Hope this helps.
If you need a clearer description, I'll send you a Word file with diagrams etc.

Bruce

J

#### jmGiraud

To make it clear, Art Boudreau refers to CRC. This formula calculates the volume of a spherical segment. In your case (probably) the empty part of the sphere. This formula is OK and is simpler than the Perry one.

If your tank is a cylindrical horizontal one and you may ignore the 'end dishes', your situation is a partialy filled pipe.

At this point, as an Instrumentation Man you would measure the diameter (D) as a constant and the level (h) as a variable. Then comes an approximation for the area (S) of the filled circular segment.

S= 0.7854.C.D^2
where
C= (((((a6x+a5)x+a4)x+a3)x+a2)x+a1)x+a0
and
x= h/D
The coefficients:
a0= -0.0004
a1= 0.2744
a2= 2.968
a3= -4.6
a4= 3.9314
a5= -1.573
a6= 0.0...

The order of the polynomial could be increased but for what purpose, C is within ± .001
[email protected]

A

A

#### Anonymous

Also what about the expected change in volume for an increase of 10 degrees Fareinheit if the fluid is gasoline?

What would be the change in volume of both fluids if a tank contains 500 gallons of water and 9,500 gallons of gasoline with the same temperature change?

Thanks LF

See Chemical Processing Magazine, November 2002, "Computing Fluid Tank Volumes", By Dan Jones. Calculates the exact volume of fluid in almost any horizontal or vertical cylindrical or elliptical tank. Dan