Geoscience Reference
In-Depth Information
TUBE CIRCUMFERENCE
The tube circumference (
S
), which is independent of the degree of filling, comprises
the components of a rectangle, two circle quadrants plus half an ellipse. By setting this
filled circumference equal to the circumference of a notional circle with 100% degree
of filling and radius
R
, a formula with several unknowns arises.
(
)
2
απ
(D.1)
S
r
MR
2
r
+
π
where:
b
α
=
r
35
72
2
15
2
4
1
+⋅
+
mm
m
2
M
r
r
⋅
πα
1
+
m
ab
ab
1
1
α
−
m
=
=
+
α
where:
S
=
circumference of the tube [m];
M
=
half circumference (approximate) of a half ellipse [m];
b
=
half height of an ellipse [m];
a
=
half width of an ellipse [m];
r
=
radius of curvature of the ellipse along the horizontal axis
=
the radius of the
quadrants [m];
R
=
the radius of the notional circle at 100% degree of filling [m].
TUBE CROSS-SECTIONAL AREA
The filled cross-sectional area of the tube depends on the degree of filling and
comprises a half rectangle, two circle quadrants plus half an ellipse. By setting the
calculated cross-sectional area equal to the product of the degree of filling and the
cross-sectional area of the notional circle (at 100% filling) the following formula,
with the same unknowns, is generated.
1
+
⎛
⎝
1
⎞
⎠
32
r
22
2
=
2
(D.2)
f
R
2
⎛
⎝
2
+⋅
α
2
⋅
r
r
r
+
⎛
⎝
⎛
⎝
π
r
f
R
r
πα
2
2
where:
A
=
cross-sectional area [m
2
];
f
=
degree of filling [-].
