AS 3778.2.4-2007

1-AS 3778.2.4-2007 Measurement of water flow in open channels Part 2.4: General - Estimation of uncertainty of a flow rate measur
4-PREFACE
5-CONTENTS
6-INTRODUCTION
7-1 Scope
7-2 Normative references
7-3 Terms and definitions
9-4 Symbols and abbreviated terms
9-4.1 Symbols
13-4.2 Subscripts
14-5 Evaluation of the uncertainty in a measurement process
15-6 Type A evaluations of uncertainty
15-6.1 General considerations
15-6.2 Calculation procedure
16-7 Type B evaluation of uncertainties
16-7.1 General considerations
16-7.2 Calculation procedure
16-7.3 Rectangular probability distribution
17-7.4 Normal probability distribution
17-7.5 Triangular probability distribution
17-7.6 Bimodal probability distribution
17-7.7 Assigning a probability distribution
17-7.8 Asymmetric probability distributions
18-8 Sensitivity coefficients
18-8.1 General
18-8.2 Analytical solution
18-8.3 Numerical solution
19-9 Combination of uncertainties
20-10 Expression of results
20-10.1 Expanded uncertainty
21-10.2 Uncertainty budget
23-Annex A (normative) Step-by-step procedure for calculating uncertainty
23-A. 1 Dimensional and non-dimensional uncertainty
23-A. 2 Mathematical relationship
23-A. 3 Standard uncertainty
24-A. 4 Sensitivity coefficients
24-A. 5 Combined uncertainty
24-A. 6 Unreliable input quantities
25-A. 7 Expanded uncertainty
25-A. 8 Expression of results
26-Annex B (normative) Probability distributions
28-Annex C (normative) Coverage factors
30-Annex D (informative) Basic statistical concepts for use in Type A assessments of uncertainty
30-D.1 Mean of a set of data,
30-D.2 Experimental standard deviation, s, of a set of data
31-D.3 Degrees of freedom, ν, associated with a sample variance or standard deviation
31-D.4 Standard uncertainty, xu, of a sample mean based on the sample standard deviation
31-D.5 Standard uncertainty, xu, of the sample mean based on a standard deviation derived from past experience
31-D.6 Standard uncertainty, usm, of a single value based on past experience
32-D.7 Pooled standard deviation, spo, from several sets of data
32-D.8 Degrees of freedom, vpo, associated with a pooled standard deviation
32-D.9 Expanded uncertainty, xU, of a sample mean based on the sample standard deviation
33-D.10 Expanded uncertainty, xU, of a sample mean based on a standard deviation derived from past experience
33-D.11 Expanded uncertainty, Usm, of a single value
33-D.12 Tolerance interval for individual measurements
34-D.13 Detection of outliers
35-D.14 Worked examples
42-Annex E (informative) Measurement uncertainty sources
42-E.1 Categories of uncertainty sources
42-E.2 Calibration uncertainty
42-E.3 Data acquisition uncertainty
43-E.4 Data processing uncertainty
43-E.5 Uncertainty due to methods
44-Annex F (informative) Correlated input variables
46-Annex G (informative) Examples
46-G.1 Example 1 - A critical flow nozzle is used to measure the mass flow of air in a calibration rig
48-G.2 Example 2 - Comparing two flow-rates measured with the same meter
53-G.3 Example 3 - Computation of the uncertainty of flow measurement made by an orifice plate
59-G.4 Example 4 - Computation of uncertainty in a flow (discharge) measurement made by a velocity- area survey using a current meter
61-G.5 Example 5 - Computation of uncertainty in a flow (discharge) measurement made using weirs and flumes
64-Annex H (informative) The calibration of a flow meter on a calibration rig
64-H.1 General
64-H.2 Calibration rig uncertainty
64-H.3 Use of the calibration rig
67-Annex I (informative) Type A and Type B uncertainties in relation to contributions to uncertainty from random and systematic sources of uncertainty
68-Annex J (informative) Special situations using two or more meters in parallel
70-Annex K (informative) Alternative technique for uncertainty analysis
71-Bibliography