Rice Lake Weigh Modules/Mount Assemblies - Manual (Page 18)

SYSTEM DESIGN
1-16
Calculating Tank Volumes
Wedge II
Volume =
hAB
2
A
h
B
Frustum of Pyramid
Volume =
h
6
2 AB
+
Ab
+
aB
+
2ab
( )
a
h
B
A
b
Angle of Repose
When a granular material is dropped from above onto a flat surface
it tends to form a cone, as shown in Figure 1-24. The shape of this
cone is described by the angle of repose,
α
, which is a characteristic
of the material. The angle of repose varies somewhat with particle
size, moisture content, etc. The relationship between
α
, h, and D
(see Figure 1-24) is:
h
=
D tan
α
2
D
h
α
Figure 1-24
The volume of any cone is:
height
3
x area of base
In calculating the volume of material in a vessel, an adequate
approximation can be made by adding 1/3 of the height of the cone
to the height of material up to the cone.
For example, in Figure 1-25, assume the height of the material in
the cylindrical vessel to be 15'+1.5'=16.5 feet.
Thus the volume is calculated using the following formula:
Volume =
π
4
D 2 h =
13'
4.5'
15'
Figure 1-25
x (13) 2 x 16.5 = 2190 cubic feet
3.14
4