DP Flow Measurement Uncertainty Calculator (ISO 5167)
Find the uncertainty of an orifice, nozzle or venturi flow measurement by combining the uncertainties of each input with the sensitivity coefficients given in ISO 5167-1, and see which input dominates.
- (δq/q)² = (δC/C)² + (δε/ε)² + [2/(1 − β⁴)]²(δd/d)² + [2β⁴/(1 − β⁴)]²(δD/D)² + ¼(δΔP/ΔP)² + ¼(δρ/ρ)²
- δq/q = ± 0.602 %
Uncertainty budget
| Input | Input uncertainty | Sensitivity | Contribution | Share of variance |
|---|---|---|---|---|
| C | 0.5 % | 1.000 | 0.5 % | 69 % |
| ε | 0 % | 1.000 | 0 % | 0 % |
| Bore d | 0.07 % | 2.298 | 0.161 % | 7.14 % |
| Pipe D | 0.4 % | 0.298 | 0.119 % | 3.91 % |
| ΔP | 0.5 % | 0.500 | 0.25 % | 17.2 % |
| Density | 0.2 % | 0.500 | 0.1 % | 2.76 % |
ISO 5167-1 Uncertainty Equation
Each δx/x is the relative uncertainty of an input at the same confidence level, and the terms are combined in quadrature as ISO 5167-1 describes. The C uncertainty comes from the relevant part of ISO 5167 (about 0.5 % for orifice plates with β from 0.2 to 0.6). The DP uncertainty is that of the transmitter at the operating DP, which grows at low flow. Extra uncertainty for short straight lengths is added arithmetically, not in quadrature.
Worked example
An orifice with β = 0.6, C ± 0.5 %, bore ± 0.07 %, pipe ± 0.4 %, DP ± 0.5 % and density ± 0.2 % gives about ± 0.60 % of flow; C is the largest contributor.
Frequently Asked Questions
Why does density count only half?
Mass flow is proportional to √(ΔP × ρ), so a relative error in ρ gives half that relative error in flow.
Why is pipe diameter less important than bore?
Its sensitivity is 2β⁴/(1 − β⁴), small at moderate β, while the bore has 2/(1 − β⁴), more than 2.
Is this the total measurement uncertainty?
It covers the primary element and inputs. Add installation effects and, for gases, pressure and temperature uncertainty in density.
Learn more on the blog
Mistakes in DP flow measurement
A practical, field focused guide on instrumentationblog.in that explains the theory behind this calculator and how engineers apply it on real plants.
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