Tokyo Keiki UFP-20, Installation & Operation Manual

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3-14
( )
( )
( )
V
V
k
velocity flow average Actual
flowmeter ultrasonic by obtained velocity flow Average
t coefficien correction volume Flow
=
(8)
Next, flow volume q can be expressed as shown in formula (9) when the cross sectional
area of the pipe is defined as A.
( )
( )
2
2
2
2
cos sin 2 4
1
cos sin 2
4
1
τ
θ θ
π
τ θ θ
π
−
∆
⋅
















⋅ ⋅
⋅
⋅
⋅ =
∆ ⋅
− ⋅ ⋅ ⋅
⋅
⋅
⋅ = ⋅ = ⋅ =
to
t d
d
k
t
to
d
d
k k
V
A V A q
(9)
Scale factor
Therefore, if the scale factor in formula (9) is calculated beforehand, flow volume q can
be calculated from the actual measurement values of formulas (4) and (5). In other
words, formula (9) shows that the affects of changes in the velocity of sound in water
can be eliminated by measuring ∆t and to.
Next, the flow volume correction coefficient k, expressing the relationship between the
measurement velocity V and the actual average velocity
V
as shown by formula (8),
changes depending on the Reynolds Number. Therefore, with this ultrasonic flowmeter,
the velocity V obtained from formula (7) using the ultrasonic flowmeter is further used to
obtain a temporary average velocity
V
using formula (10). The Reynolds Number Re
expressed in formula (11) is then calculated using this temporary value.
V V
≒
(10)
ν
V d
Re
⋅
=
( )
viscosity Kinematic ;
ν
(11)
Finally, the Reynolds Number Re calculated using formula (11) is used to calculate a
flow volume correction coefficient k, correlated to the flow velocity, from the formula of
G.E. Birger.