Page 12 • MNKS025 ║ Issue/Rev. 0.1 (11/18)
MPU Series C I/O/M Manual
Product Overview
2.2.1.
Transit Time Measurement
To measure gas flow and velocity of sound (VOS), the MPU employs the fact that sound
travels faster with the gas flow than against it. The figure below shows a top view of a
pipe with gas flow. The gas flow velocity is V, ϴ is the angle the sound beams make with
the pipe wall, A and B are the positions of the transducers and L is the distance between
transducer A and B. Tu and Td are the times of flight up- and downstream respectively.
These travel times, together with the geometry of the system, i.e. transducer mount-
ing and pipe diameter, are all that is needed to calculate the gas flow velocity and the
velocity of sound for each path.
V
A
B
θ
L
T
d
T
u
Top View of Path; Travel Times
The sound will travel slower upstream and faster downstream because of the velocity
component of the gas flow in the direction of the sound path. This yield
and
where c is the velocity of sound in the gas and v is the gas flow velocity.
)
cos(
θ
v
c
L
T
d
+
=
)
cos(
θ
v
c
L
T
u
−
=
d
u
d
u
T
T
T
T
L
v
−
⋅
=
)
cos(
2
θ
d
u
d
u
T
T
T
T
L
c
+
⋅
=
2
)
cos(
θ
v
c
L
T
d
+
=
)
cos(
θ
v
c
L
T
u
−
=
d
u
d
u
T
T
T
T
L
v
−
⋅
=
)
cos(
2
θ
d
u
d
u
T
T
T
T
L
c
+
⋅
=
2
Summary of Contents for Smith Meter MPU 1600c
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