11/28/2016 Tank Volume Calculator
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Tank Volume Calculator
Tank Volume & Fill Calculator Tank Schematic: Horizontal Cylinder
Tank Type: Horizontal Cylinder
(inside dimensions) Feet Inches
Length (l) =
Diameter (d) =
Filled Depth (f) =
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Answer:
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Estimate the total and filled volumes of tanks such as
oil tanks and water tanks. Assumes inside
dimensions of the tank.
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*Actual fill volumes will differ. Tank volume
© CalculatorSoup calculations are based on tank geometries shown
below. These tank shapes are calculated assuming
Share this Calculator & Page exact geometric solid shapes such as cylinders,
circles and spheres. Actual water and oil tanks may
not be perfect geometric shapes or might have other
features not accounted for here so, these calculations
should only be considered estimates.
Methods to calculate the volume of tanks and the volume of a liquid inside a
tank.
These calculations will give you cubic measures such as ft3 or m3 depending on your units of
measure.
Total volume of a cylinder shaped
Horizontal Cylinder Tank tank is the area, A, of the circular
end times the length, l. A = πr2
where r is the radius which is equal
to 1/2 the diameter or d/2.
Therefore:
V(tank) = πr2l
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The filled volume of a horizontal
cylinder tank is calculated by first
finding the area, A, of a circular
segment and multiplying it by the
length, l.
Area of the circular segment, the
grey shaded area, is A = (1/2)r2(θ
sinθ) where θ = 2*arccos(m/r) and θ
is in radians. Therefore,
V(segment) = (1/2)r2(θ sinθ)l. If
the fill height f is less than 1/2 of d
then we use the segment created
from the filled height and V(fill) =
V(segment). However, if the fill
height f is greater than 1/2 of d then
we use the segment that is created
by the empty portion of the tank
and subtract it from the total
volume to get the filled volume;
V(fill) = V(tank) V(segment).
Total volume of a cylinder shaped
Vertical Cylinder Tank tank is the area, A, of the circular
end times the height, h. A = πr2
where r is the radius which is equal
to d/2. Therefore:
V(tank) = πr2h
The filled volume of a vertical
cylinder tank is just a shorter
cylinder with the same radius, r,
and diameter, d, but height is now
the fill height or f. Therefore:
V(fill) = πr2f
Total volume of a rectangular prism
Rectangle Tank shaped tank is length times width
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11/28/2016 Tank Volume Calculator
times height. Therefore,
V(tank) = lwh
The filled volume of a rectangular
tank is just a shorter height with the
same length and width. The new
height is the fill height or f.
Therefore:
V(fill) = lwf
Volume of an oval tank is
Horizontal Oval Tank calculated by finding the area, A, of
the end, which is the shape of a
stadium, and multiplying it by the
length, l. A = πr2 + 2ra and it can
be proven that r = h/2 and a = w
h where w>h must always be true.
Therefore:
V(tank) = (πr2 + 2ra)l
Volume of fill of a horizontal oval
tank is best calculated if we
assume it is 2 halves of a cylinder
separated by a rectangular tank.
We then calculate fill volume of 1)
a Horizontal Cylinder Tank where
l = l, f = f, and diameter d = h, and
2) a Rectangle Tank where l = l, f =
f, and rectangle width w is a = w h
of the oval tank.
V(fill) = V(fillhorizontalcylinder)
+ V(fillrectangle)
Volume of an oval tank is
Vertical Oval Tank calculated by finding the area, A, of
the end, which is the shape of a
stadium, and multiplying it by the
length, l. A = πr2 + 2ra and it can
be proven that r = w/2 and a = h
w where h>w must always be true.
Therefore:
V(tank) = (πr2 + 2ra)h
Volume of fill of a vertical oval tank
is best calculated if we assume it is
2 halves of a cylinder separated by
a rectangular tank. With r = w/2 =
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11/28/2016 Tank Volume Calculator
hieght of the semicircle ends, we
can define 3 general fill position
areas.
Fill, f < r
We calculate fill volume using
the circular segment method,
as in a Horizontal Cylinder
Tank, for the filled portion.
Fill, f > r and f < (r+a)
The filled volume is exactly
1/2 of the cylinder portion plus
the volume of fill inside the
rectangular portion.
Fill, f > (r+a) and f < h
We calculate fill volume using
the circular segment method,
as in a Horizontal Cylinder
Tank, for the empty portion.
Volume will be V(tank)
V(segment).
We treat a capsule as a sphere of
Horizontal Capsule Tank diameter d split in half and
separated by a cylinder of diameter
d and height a. Where r = d/2.
V(sphere) = (4/3)πr3, and
V(cylinder) = πr2a, therefore
V(capsule) = πr2((4/3)r + a)
Volume of fill for a horizontal
capsule is done by using the
circular segment method for the
Horizontal Cylinder and, with a
similar approach, using calculations
of a spherical cap for the sphere
section of the tank where,
V(spherical cap) = (1/3)πh2(3R h)
We treat a capsule as a sphere of
Vertical Capsule Tank diameter d split in half and
separated by a cylinder of diameter
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d and height a. Where r = d/2.
V(capsule) = πr2((4/3)r + a)
Volume of fill for a vertical capsule
is calculated in a fashion similar to
the method used for the Vertical
Oval Tank where r = d/2 = height of
each hemisphere end.
Fill, f < r
We calculate fill volume using
the spherical cap method, for
the filled portion.
Fill, f > r and f < (r+a)
The filled volume is exactly
1/2 of the sphere portion plus
the volume of fill inside the
vertical cylinder portion.
Fill, f > (r+a) and f < h
We calculate fill volume using
the spherical cap method for
the empty portion. Volume
will be V(tank) V(spherical
cap).
Cite this content, page or calculator as:
Furey, Edward "Tank Volume Calculator"; from http://www.calculatorsoup.com Online Calculator
Resource.
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