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AS 3778.2.4-2007


Measurement of water flow in open channels, Part 2.4: General — Estimation of uncertainty of a flow rate measurement

establishes general principles and describes procedures for evaluating the uncertainty of a fluid flow-rate or quantity.
Published: 06/08/2007
Pages: 65
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Table of contents
Cited references
Content history
Table of contents
About this publication
1 Scope
2 Normative references
3 Terms and definitions
4 Symbols and abbreviated terms
4.1 Symbols
4.2 Subscripts
5 Evaluation of the uncertainty in a mea surement process
6 Type A evaluations of uncertainty
6.1 General considerations
6.2 Calculation procedure
7 Type B evaluation of uncertainties
7.1 General considerations
7.2 Calculation procedure
7.3 Rectangular probability distribution
7.4 Normal probability distribution
7.5 Triangular probability distribution
7.6 Bimodal probability distribution
7.7 Assigning a probability distribution
7.8 Asymmetric probability distributions
8 Sensitivity coefficients
8.1 General
8.2 Analytical solution
8.3 Numerical solution
9 Combination of uncertainties
10 Expression of results
10.1 Expanded uncertainty
10.2 Uncertainty budget
Annex A
A.1 Dimensional and non-dimensional uncertainty
A.2 Mathematical relationship
A.3 Standard uncertainty
A.3.1 General
A.3.2 Type A evaluations — Standard deviation of the mean of repeated measurements
A.3.3 Type B evaluations — Based on subjective assessment and experience
A.3.3.1 Rectangular probability distribution
A.3.3.2 Normal probability distribution
A.4 Sensitivity coefficients
A.4.1 General
A.4.2 Dimensional
A.4.3 Non-dimensional
A.5 Combined uncertainty
A.5.1 General
A.5.2 Dimensional
A.5.3 Non-dimensional
A.6 Unreliable input quantities
A.7 Expanded uncertainty
A.8 Expression of results
Annex B
Annex C
Annex D
D.1 Mean of a set of data, x¯
D.2 Experimental standard deviation, s, of a set of data
D.3 Degrees of freedom, ν, associated with a sample variance or standard deviation
D.4 Standard uncertainty, ux¯, of a sample mean based on the sample standard deviation
D.5 Standard uncertainty, ux¯, of the sample mean based on a standard deviation derived from past experience
D.6 Standard uncertainty, usm, of a single value based on past experience
D.7 Pooled standard deviation, spo, from several sets of data
D.8 Degrees of freedom, vpo, associated with a pooled standard deviation
D.9 Expanded uncertainty, Ux¯, of a sample mean based on the sample standard deviation
D.10 Expanded uncertainty, Ux¯, of a sample mean based on a standard deviation derived from past experience
D.11 Expanded uncertainty, Usm, of a single value
D.12 Tolerance interval for individual measurements
D.13 Detection of outliers
D.14 Worked examples
D.14.1 Mean, variance, standard deviation, degrees of freedom and coefficient of variation
D.14.1.1 General
D.14.1.2 Mean
D.14.1.3 Variance
D.14.1.4 Standard deviation
D.14.1.5 Degrees of freedom
D.14.1.6 Coefficient of variation
D.14.2 Standard and expanded uncertainties of a mean using sample standard deviation
D.14.2.1 General
D.14.2.2 Standard uncertainty of the mean
D.14.2.3 Expanded uncertainty of the mean at the 95 % confidence level
D.14.3 Standard and expanded uncertainties of a single value
D.14.3.1 General
D.14.3.2 Standard uncertainty
D.14.3.3 Expanded uncertainty
D.14.4 Pooled standard deviation from several sets of data
D.14.4.1 General
D.14.4.2 Pooled standard deviation
D.14.4.3 Pooled degrees of freedom
D.14.5 Expanded uncertainty of a sample mean based on a standard deviation from past experience
D.14.5.1 General
D.14.5.2 Standard uncertainty
D.14.5.3 Expanded uncertainty
D.14.6 Tolerance interval for individual values
D.14.7 Rejection of outliers
Annex E
E.1 Categories of uncertainty sources
E.2 Calibration uncertainty
E.3 Data acquisition uncertainty
E.4 Data processing uncertainty
E.5 Uncertainty due to methods
Annex F
Annex G
G.1 Example 1 — A critical flow nozzle is used to measure the mass flow of air in a calibration rig
G.1.1 Mathematical model
G.1.2 Contributory variances
G.1.2.1 Uncertainty in the calibration coefficient, φC
G.1.2.2 Uncertainty in the measurement of upstream pressure, p0
G.1.2.3 Uncertainty in the measurement of upstream temperature, T0
G.1.2.4 Combined uncertainty
G.2 Example 2 — Comparing two flow-rates measured with the same meter
G.2.1 General
G.2.2 Mathematical model
G.2.3 Contributory variances
G.2.4 Uncertainty in density measurement
G.2.5 Uncertainty in manometer readings
G.2.6 Combined uncertainty in the flow ratio, ΦF
G.3 Example 3 — Computation of the uncertainty of flow measurement made by an orifice plate
G.3.1 General
G.3.2 The mathematical model
G.3.3 Contributory variances
G.3.4 Uncertainty in measured pipe diameter, dp,0
G.3.5 Uncertainty in measured orifice diameter, do,0
G.3.6 Uncertainty in temperature, T0,x
G.3.7 Uncertainty in the fluid temperature, Top
G.3.8 Uncertainty in density, ρ
G.3.9 Uncertainty in pressure difference, Δp
G.3.10 Uncertainty in thermal expansion coefficient, λ
G.3.11 Uncertainty in fluid viscosity, μ
G.3.12 Uncertainty in the Reader-Harris/Gallagher (1998) equation
G.3.13 Combined uncertainty in the flow-rate
G.4 Example 4 — Computation of uncertainty in a flow (discharge) measurement made by a velocity-area survey using a current meter
G.4.1 Mathematical model
G.4.2 Contributory variances
G.4.3 Combined uncertainty
G.5 Example 5 — Computation of uncertainty in a flow (discharge) measurement made using weirs and flumes
G.5.1 The mathematical model
G.5.2 Contributory variances
Annex H
H.1 General
H.2 Calibration rig uncertainty
H.3 Use of the calibration rig
H.3.1 General
H.3.2 Calibration at a number of different flowrates with n measurements per flowrate
Annex I
Annex J
Annex K
Cited references in this standard
Content history
DR 07107
AS 3778.2.4-2007 REC:2022