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<2. PRINCIPLES OF OPERATION>
2-1
IM 12T03A01-02E
2. PRINCIPLES OF OPERATION
2.1 Measuring Principle
2.1.1 Density Detector
Model VD6D Density Detector is a vibration type density meter. Measuring principle is that the
lateral free oscillation of a pipe is a function of the density of the liquid contained in the pipe.
Assuming that the pipe is filled with a liquid as shown in Figure 2.1, the lateral free oscillation of
the pipe can be shown as the following equation:
Joint
l
D
2
D
1
Joint
Figure 2.1 Pipe Filled with Liquid
f
x
: Free transfers oscillation frequency for ρ
x
[Hz]
C
: Constant determined by oscillation mode
l
: Oscillating pipe length [m]
E
: Young's modulus of pipe [kg/m 3 ]
ρ
l
: Density of pipe material [kg/cm 3 ]
ρ
x
: Density of liquid measured [kg/cm 3 ]
D
1
: Pipe outside diameter [m]
D
2
: Pipe inside diameter [m]
(1) f
x
=
C
4 l 2
E
ρ
l
√ √
D
12
+ D
22
1 + x
ρ
x
ρ
l
D
22
D
12
- D
22
In equation (1), the values other than ƒx and ρx are determined by the pipe material and
construction. Thus, the density ρx of the liquid can be obtained by measuring the free transfers
oscillation frequency ƒ
x
.
2.1.2 Density Converter
The density converter computes the liquid density using the oscillation frequency signal and
voltage of the temperature.
Each value of l, E, ρl, D1, D2 or ρx in equation (1) is a function of liquid temperature, hence the
value of ƒ
x
is also a function of temperature. To obtain the correct density, the factors A(t) and B(t)
depending temperature should be previously compensated for the temperature as follows.
where, A
(t)
= A
1
( 1.0060 - 1.9814 x 10 -4 • T - 9.7683 x 10 -8 • T 2 )
B
(t)
= B
1
{ 1 + 4.5 x 10 -5 ( T - 30 ) }
A
(t)
= ( A + 131072 ) / 100
B
1
= B / 300
T : Liquid temperature (°C)
(2)
A
(t)
l +
ρ
x
B
(t)
√
f
x
=
(Note): Both A and B are constants of the detector which has inherent values.
5th Edition : Dec. 11, 2015-00