E1C05 09/14/2010
14:36:26 Page 167
Voltmeter
Resolution:
10 mV
Accuracy:
within 0.001% of reading
Transducer
Range:
Æ5 psi ($Æ0.35 bar)
Sensitivity:
1 V/psi
Input power:
10 VDC Æ 1%
Output:
Æ5 V
Linearity error:
within 2.5 mV/psi over range
Sensitivity error: within 2 mV/psi over range
Resolution:
negligible
KNOWN Instrument specifications
ASSUMPTIONS Values at 95% probability; normal distribution of errors
FIND u c for each device and u d for the measurement system
SOLUTION The procedure in Figure 5.2 is used for both instruments to estimate the designstage uncertainty in each. The resulting uncertainties are then combined using the RSS approximation to estimate the system u d .
The uncertainty in the voltmeter at the design stage is given by Equation 5.3 as
u d
ð Þ E ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
u o
ð Þ
2
E þ u c
ð Þ
2
E
q
From the information available,
u 0
ð Þ E ¼ 5 mV
For a nominal pressure of 3 psi, we expect to measure an output of 3 V. Then,
u c
ð Þ E ¼ 3 V Â 0:00001
ð
Þ ¼ 30 mV
so that the design-stage uncertainty in the voltmeter is
u d
ð Þ E ¼ 30:4 mV
The uncertainty in the pressure transducer output at the design stage is also found using
Equation 5.2. Assuming that we operate within the input power range specified, the instrument
output uncertainty can be estimated by considering the uncertainty in each of the instrument
elemental errors of linearity, e 1 , and sensitivity, e 2 :
u c
ð Þ p ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
u 2
1 þ u 2
2
p
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2:5 mV=psi  3 psi
ð
Þ
2 þ 2 mV=psi  3 psi
ð
Þ
2
q
¼ 9:61 mV
Since (u 0 ) % 0 V/psi, the design-stage uncertainty in the transducer in terms of indicated voltage is
u d
ð Þ p ¼ 9:61 mV.
5.3 Design-Stage Uncertainty Analysis 167
14:36:26 Page 167
Voltmeter
Resolution:
10 mV
Accuracy:
within 0.001% of reading
Transducer
Range:
Æ5 psi ($Æ0.35 bar)
Sensitivity:
1 V/psi
Input power:
10 VDC Æ 1%
Output:
Æ5 V
Linearity error:
within 2.5 mV/psi over range
Sensitivity error: within 2 mV/psi over range
Resolution:
negligible
KNOWN Instrument specifications
ASSUMPTIONS Values at 95% probability; normal distribution of errors
FIND u c for each device and u d for the measurement system
SOLUTION The procedure in Figure 5.2 is used for both instruments to estimate the designstage uncertainty in each. The resulting uncertainties are then combined using the RSS approximation to estimate the system u d .
The uncertainty in the voltmeter at the design stage is given by Equation 5.3 as
u d
ð Þ E ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
u o
ð Þ
2
E þ u c
ð Þ
2
E
q
From the information available,
u 0
ð Þ E ¼ 5 mV
For a nominal pressure of 3 psi, we expect to measure an output of 3 V. Then,
u c
ð Þ E ¼ 3 V Â 0:00001
ð
Þ ¼ 30 mV
so that the design-stage uncertainty in the voltmeter is
u d
ð Þ E ¼ 30:4 mV
The uncertainty in the pressure transducer output at the design stage is also found using
Equation 5.2. Assuming that we operate within the input power range specified, the instrument
output uncertainty can be estimated by considering the uncertainty in each of the instrument
elemental errors of linearity, e 1 , and sensitivity, e 2 :
u c
ð Þ p ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
u 2
1 þ u 2
2
p
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2:5 mV=psi  3 psi
ð
Þ
2 þ 2 mV=psi  3 psi
ð
Þ
2
q
¼ 9:61 mV
Since (u 0 ) % 0 V/psi, the design-stage uncertainty in the transducer in terms of indicated voltage is
u d
ð Þ p ¼ 9:61 mV.
5.3 Design-Stage Uncertainty Analysis 167