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