Tools › Fluids and Heat Transfer › Pipe Flow › Flow Measurement: Orifices, Nozzles, Weirs and Flumes › Example
A 4-in Schedule 40 water line with a β = 0.6 orifice plate and flange taps at 100 gpm, and the NBS 90° V-notch weir example (1 ft head, 1 ft notch height, 2.5 ft channel)
| Tool | Flow Measurement: Orifices, Nozzles, Weirs and Flumes |
| Source | Kulin, G., and Compton, P. R. (1975). A Guide to Methods and Standards for the Measurement of Water Flow. NBS Special Publication 421, National Bureau of Standards, Washington, DC (section 4.4.2.2, p. 33, and Figures 4.3 to 4.5); U.S. Department of the Interior, Bureau of Reclamation (2001). Water Measurement Manual, 3rd ed. (chapter 7, section 7, eq. 7-3, Figures 7-6a, 7-6b, 7-7); International Organization for Standardization (2003). ISO 5167-2:2003 (the Reader-Harris/Gallagher equation, cited). |
| Level | Professional |
Problem
Water at 60 °F and 50 psia flows at 100 gpm through a 4-in Schedule 40 line (ID 4.026 in) fitted with a sharp-edged orifice plate of bore 2.4156 in (β = 0.6) and flange taps. Find the Reynolds number, the Reader-Harris/Gallagher discharge coefficient, the differential pressure, the permanent pressure loss, the flow turndown for a transmitter spanning 100:1 in differential and the ISO 5167 combined uncertainty. Separately, a 90° V-notch weir with its point 1.00 ft above the invert in a 2.50 ft channel runs at a head of 1.00 ft: rate it by the Kindsvater-Shen relation with the partially contracted coefficient and compare the Cone equation.
Inputs to Enter
- Orifice: water 60 °F, p1 50 psia; 4 in Sch 40 (D 4.026 in); bore 2.4156 in; flange taps; solve the differential from Q = 100 gpm; span ratio 100; U(D) 0.3 %, U(d) 0.07 %, U(Δp) 1 %, U(ρ) 0.2 %, U(C) and U(ε) by the standard
- V-notch: h1 1.00 ft, θ 90°, partially contracted rating, B 2.5 ft, p 1.0 ft
Answers
- Orifice: ρ 62.37 lb/ft³, μ 1.121 cP; Re_D = 70,019; L1 = L2 = 25.4/102.26 = 0.2484; C = 0.61220; Δp = 21.21 in. w.g.; velocity 2.52 ft/s in the pipe, 7.00 ft/s in the bore; permanent loss 0.626 Δp = 13.28 in. w.g.
- Rangeability: at Δp/100 = 0.212 in. w.g. the flow is 10.35 gpm with C 0.6337 (Re 7,247): turndown 9.66
- Uncertainty: U(C) 0.5 % (0.2 ≤ β ≤ 0.6), U(ε) 0; combined 0.738 % = 0.74 gpm
- V-notch: h1/p 1.0, p/B 0.4; k_h 0.00286 ft (Figure 7-6a), C_e 0.5986 (Figure 7-7, P/B 0.4 curve at H/P 1.0); Q = 4.2785 · 0.5986 · tan 45° · 1.00286^2.5 = 2.579 ft³/s (NBS prints 2.57); Cone equation 2.49 h^2.48 = 2.49 ft³/s
Notes
The tool's default inputs are this orifice; choose the V-notch weir in the element dropdown for the second part (its defaults are the NBS case). The orifice case is illustrative (stated on the page) and is checked against an independent numpy implementation and the open-source fluids library; the V-notch coefficients were digitized from the NBS SP 421 figures (checks in test_flow_measurement.php, 1,134 checks).