Volumetric Flow Rate Measurement - ABB 3000 Series Instruction Manual

This may be expressed mathematically as -
(Equation #1)
where:
E = induced electrode voltage
s
B = magnetic field strength
D = meter pipe diameter
α = dimensionless constant
V = liquid velocity
Thus, the metered liquid constitutes a continuous series of conductive liquid disks moving through a
magnetic field. The more rapid the rate of liquid flow, the greater the instantaneous value of signal
voltage as monitored at the meter electrodes.

4.1.2 Volumetric Flow Rate Measurement

The Flowmeter is a volumetric flow rate measuring instrument. This can be shown by substituting the
physical equivalent of liquid velocity into equation #1 as follows:
(Equation #2)
Substituting for V in equation #1
and solving for Q:
Since B = β E and since α, D and β are constant:
r
(Equation #3)
where:
Q = volumetric flow rate
A = cross-sectional area
D = pipe section diameter
E = induced signal voltage
s
E = reference voltage
r
B = magnetic flux density
α = dimensionless constant
β & γ = dimensional constant
V = liquid velocity
Therefore, volumetric flow rate is directly proportional to the induced signal voltage as measured by
the meter.
4-2
10DS3111A INSTRUCTION MANUAL
1
E s = BDV
α
Q = 4 Q
V =
2
πD
A
4 Q
E s = 1 BD
2
α πD
2
∴ Q = παD
• E
s
4 B
Q = γ E
s
E
r