DH Instruments FPG8601, Operation And Maintenance Manual

Page: 27 / 166

2. FPG THEORY OF OPERATION
Page 15 © 2007 DH Instruments, a Fluke Company
2.6 SIMPLIFIED FORMULA FOR CALCULATING
DIFFERENTIAL PRESSURE
The calculation of differential pressure is made following the basic formula:
Δ
P = F/A
eff.
(
θ
)
VARIABLE DEFINITION
Δ
P
Differential pressure between the upper and lower chambers in Pa.
F
Force measured by the load cell in counts (1 count = 1 mg).
A
eff.
(
θ
)
Effective area of the piston-cylinder at the operating temperature,
θ
.
The value is expressed in m
2
.
The force, F, measured by the load cell when it displays a number of counts, N, can be calculated using a
calibration coefficient, K
cal
, following:
F = K
cal.
. N
VARIABLE DEFINITION
K
cal.
Calibration coefficient of the load cell. This value contains any
necessary slope correction for the load cell determined by the
internal calibration (see Section 5.3). The air density and local
gravity present at the time the calibration was performed are also
quantified by this value. The calibration factor is expressed in
Newtons/ Count (1 count = 1 mg).
N
Number of counts output by the load cell representing the force
measured. One count represents the force corresponding to a
mass of 1 mg loaded on the load cell under the calibration
conditions.
The effective area of the piston-cylinder at temperature
θ
, can be expressed using its value at 20 °C and
the linear thermal expansivity of the piston and the cylinder materials following:
A
eff.
(
θ
) = A
eff.
(20°C) . [ 1+ (
α
p
+
α
c
) . (
θ
- 20 ) ]
VARIABLE DEFINITION
α
p
Linear thermal expansivity of the piston in K
-1
.
α
c
Linear thermal expansivity of the cylinder in K
-1
.
The piston and the cylinder are made of tungsten carbide therefore the thermal expansion coefficients are
the same;
α
p
+
α
c
= 9 . 10
-6
K
-1
. FPG Tools provides a single entry value for this combined effect in the
FPG calibration setup (see Section 6.6.3).
The simplified formula for the calculation of the differential pressure can therefore be expressed as:
Δ
P = K
cal.
. N / A
eff.
(20°C) . [ 1+ (
α
p
+
α
c
) . (
θ
- 20 ) ]