Yokogawa DM8C/VD6 Liquid Density Analyzer - Manual (Page 23)

< 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 fi lled 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
1
2 + D
2
2
1 + x
ρ
l
ρ
x
D
2
2
D
1
2 - D
2
2
In equation (1), the values other than f
x
and ρ
x
are determined by the pipe material and construction.
Thus, the density ρ
x
of the liquid can be obtained by measuring the free transfers oscillation frequency
f
x
.