Calculation examples, Calculation examples -17, System design – Rice Lake Weigh Modules/Mount Assemblies User Manual
Page 19
1-17
SYSTEM DESIGN
Calculating Tank Volumes
Example 2
If, in the last example, the vessel were filled completely, then the
volume would be:
Total Volume = Volume(a) + Volume(b) + Volume(c)
=
π
D
3
12
+
π
D
2
L
4
+
π
D
3
12
=
= 56.5 + 565.2 + 56.5
= 678.2 cu ft
Example 3
If the vessel in Example 2 is filled with linseed oil, calculate the
weight of material when the vessel is full.
From the section Density of Common Materials, we know that the
density of linseed oil is 58.5 lb/cu. ft. From Example 2, we know
that the volume of the vessel is 678.2 cubic feet.
Weight of Material =
Volume x Density
=
678.2 x 58.5
=
39,675 lb
Calculation Examples
Example 1
Calculate the volume of liquid in the horizontal tank shown below.
It has hemispherical ends and is filled to a height of 4.5 feet.
4.5'
3'
20'
3'
6'
For ease of calculation, this can be broken into 3 sections
(a)
(b)
(c)
Step 1
The volume of section (a) or (c) is given by the formula:
Volume =
where
π =
3.14,
h
=
4.5
,
D
=
6
=
=
= 47.7 cu ft
Step 2
The volume of (b) is given by the formula:
where
π
= 3.14, h = 4.5, D = 6, L = 20
=
= 565.2 – 188.4 + 77.94
= 454.7 cu ft
Step 3
Total Volume=Volume(a)+Volume (b)+Volume(c)
= 47.7 + 454.7 + 47.7
= 550.1 cu ft
3.14(6
3
)
12
3.14(6
2
) x 20
4
3.14(6
3
)
12
+
+
(182.25)
3.14
12
3.14
12
((3 x 4.5
2
x 6) – (2 x 4.5
3
))
π
12
(3h
2
D – 2h
3
)
D
2
Lcos
–1
L
√
hD – h
2
π
D
2
L
4
π
720
+ h –
( )
D
2
2h – D
D
( )
–
3.14 x 6
2
x 20cos
–1
720
3.14 x 6
2
x 20
4
–
2 x 4.5 – 6
6
( )
( )
+ 4.5 –
6
2
20
√
4.5 x 6 – 4.5
2
565.2 – 3.14cos
–1
(.5) + 30
√
6.75