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5.19 A pressure transducer outputs a voltage to a readout device that converts the signal back to pressure.
The device specifications are:
Resolution:
0.1 psi
Sensitivity error: 0.1 psi
Linearity error:
within 0.1% of reading
Drift:
less than 0.1 psi/6 months (32–90
F)
The transducer has a claimed accuracy of within 0.5% of reading. For a nominal pressure of 100 psi
at 70
F, estimate the design-stage uncertainty in a measured pressure.
5.20 For a thin-walled pressure vessel of diameter D and wall thickness t subjected to an internal
pressure p, the tangential stress is given by s ¼ pD/2t. During one test, 10 measurements of
pressure yielded a mean of 8610 lb/ft
2 with a standard deviation of 273.1 lb/ft
2 . Cylinder
dimensions are to be based on a set of 10 measurements which yielded: D ¼ 6:2 in: with
s D ¼ 0.18 in. and t ¼ 0:22 in: with s t ¼ 0.04 in. Estimate the degrees of freedom in the standard
uncertainty for stress. Determine the best estimate of stress at 95% confidence. Pressure
measurements and dimensions have a systematic uncertainty of 1% of the reading assumed at
95% confidence.
5.21 Suppose a measured normal stress contains three elemental random errors in its calibration with the
following values:
s x
ð Þ 1 ¼ 0:90 N/m
2
s x
ð Þ 2 ¼ 1:10 N/m
2
s x
ð Þ 3 ¼ 0:09 N/m
2
v 1 ¼ 21
v 2 ¼ 10
v 3 ¼ 15
Estimate the random standard uncertainty due to calibration errors with its degrees of freedom.
5.22 An experiment to determine force acting at a point on a member contains three elemental errors with
resulting uncertainties:
b x
ð Þ 1 ¼ 1:0 N
b x
ð Þ 2 ¼ 2:25 N
b x
ð Þ 3 ¼ 1:8 N
s x
ð Þ 1 ¼ 0
s x
ð Þ 2 ¼ 6:1 N
s x
ð Þ 3 ¼ 4:2 N
v 2 ¼ 17
v 3 ¼ 19
If the mean value for force is estimated to be 200 N, determine the uncertainty in the mean value at
95% confidence. Assume large degrees of freedom in the systematic uncertainties.
5.23 The area of a flat, rectangular parcel of land is computed from the measurement of the length of two
adjacent sides, X and Y. Measurements are made using a scaled chain accurate to within 0.5% (95%)
over its indicated length. The two sides are measured several times with the following results:
X ¼ 556 m
Y ¼ 222 m
s x ¼ 5:3 m
s y ¼ 2:1 m
n ¼ 8
n ¼ 7
Estimate the area of the land and state the confidence interval of that measurement at 95%.
5.24 Estimate the random standard uncertainty in the measured value of stress for a data set of 23
measurements if s ¼ 1061 kPa and s s ¼ 22 kPa. Report the best estimate for stress at 68%
confidence. Assume a normal distribution and neglect systematic errors.
202 Chapter 5 Uncertainty Analysis
14:36:33 Page 202
5.19 A pressure transducer outputs a voltage to a readout device that converts the signal back to pressure.
The device specifications are:
Resolution:
0.1 psi
Sensitivity error: 0.1 psi
Linearity error:
within 0.1% of reading
Drift:
less than 0.1 psi/6 months (32–90
F)
The transducer has a claimed accuracy of within 0.5% of reading. For a nominal pressure of 100 psi
at 70
F, estimate the design-stage uncertainty in a measured pressure.
5.20 For a thin-walled pressure vessel of diameter D and wall thickness t subjected to an internal
pressure p, the tangential stress is given by s ¼ pD/2t. During one test, 10 measurements of
pressure yielded a mean of 8610 lb/ft
2 with a standard deviation of 273.1 lb/ft
2 . Cylinder
dimensions are to be based on a set of 10 measurements which yielded: D ¼ 6:2 in: with
s D ¼ 0.18 in. and t ¼ 0:22 in: with s t ¼ 0.04 in. Estimate the degrees of freedom in the standard
uncertainty for stress. Determine the best estimate of stress at 95% confidence. Pressure
measurements and dimensions have a systematic uncertainty of 1% of the reading assumed at
95% confidence.
5.21 Suppose a measured normal stress contains three elemental random errors in its calibration with the
following values:
s x
ð Þ 1 ¼ 0:90 N/m
2
s x
ð Þ 2 ¼ 1:10 N/m
2
s x
ð Þ 3 ¼ 0:09 N/m
2
v 1 ¼ 21
v 2 ¼ 10
v 3 ¼ 15
Estimate the random standard uncertainty due to calibration errors with its degrees of freedom.
5.22 An experiment to determine force acting at a point on a member contains three elemental errors with
resulting uncertainties:
b x
ð Þ 1 ¼ 1:0 N
b x
ð Þ 2 ¼ 2:25 N
b x
ð Þ 3 ¼ 1:8 N
s x
ð Þ 1 ¼ 0
s x
ð Þ 2 ¼ 6:1 N
s x
ð Þ 3 ¼ 4:2 N
v 2 ¼ 17
v 3 ¼ 19
If the mean value for force is estimated to be 200 N, determine the uncertainty in the mean value at
95% confidence. Assume large degrees of freedom in the systematic uncertainties.
5.23 The area of a flat, rectangular parcel of land is computed from the measurement of the length of two
adjacent sides, X and Y. Measurements are made using a scaled chain accurate to within 0.5% (95%)
over its indicated length. The two sides are measured several times with the following results:
X ¼ 556 m
Y ¼ 222 m
s x ¼ 5:3 m
s y ¼ 2:1 m
n ¼ 8
n ¼ 7
Estimate the area of the land and state the confidence interval of that measurement at 95%.
5.24 Estimate the random standard uncertainty in the measured value of stress for a data set of 23
measurements if s ¼ 1061 kPa and s s ¼ 22 kPa. Report the best estimate for stress at 68%
confidence. Assume a normal distribution and neglect systematic errors.
202 Chapter 5 Uncertainty Analysis