KROHNE UFM 500 EN - Manual (Page 48)

48
11. Measuring principle
A sound wave travelling in the direction of flow of the
fluid requires less time between one fixed point and
another than one travelling in the opposite direction.
This is the principle employed to measure the flow rate
with ultrasonic waves. Different flight times are an
indication of the flow velocity of the fluid concerned.
Double-beam version: The ultrasonic sensors A + B
and A’ + B’ are located in symmetrical arrangement on
the outside of the measuring tube.
Single-beam version: The ultrasonic sensors A + B
are located in symmetrical arrangement on the outside
of the measuring tube at an angle of 180
°
.
Each line of measurement (A + B and A’ + B’) forms
an angle
ϕ
with the tube centerline.
The ultrasonic waves travel
from point A to point B at
speed
v c v cos
AB 0 m
= + × ϕ
and, conversely,
from point B to point A at speed
The following applies to the
different flight times
from points A to B
and from point B to A
The mean flow
velocity v
m
of the product
is calculated using
the last two equations:
t
AB
and t
BA
are measured continuously.
A (A’) Transmitter and receiver
B (B’) Transmitter and receiver
L Distance between ultrasonic sensors
v
m
Average flow velocity of fluid
t
AB
(v
AB
) Time of flight (propagation speed)
of sound waves from points B to A
c
0
Sound velocity in the medium (fluid)
GK Calibration constant
ϕ
Angle between tube centerline and line
of measurement
v c v cos
BA 0 m
= − × ϕ
t
L
c v cos
AB
0 m
=
+ × ϕ
t
L
c v cos
BA
0 m
=
− × ϕ
v GK
t t
t t
m
BA AB
AB BA
= Ч
−
Ч
Double-beam Single-beam