Orifice Discharge Coefficient (Reader-Harris/Gallagher, ISO 5167-2)
The discharge coefficient C of a square-edge orifice plate from the beta ratio, the pipe Reynolds number.
Example
You enter
- Pipe inside diameter (in) 4.026
- Bore / orifice diameter (in) 2.013
- Pressure taps flange
- Reynolds number entered
- Pipe Reynolds number Re_D (when entered) 200000
- Liquid flow (gpm, for the flow option) 0
- Kinematic viscosity (cSt, water about 1.0) 1
You get
- Discharge coefficient C 0.60489
- Flow coefficient C/sqrt(1 - beta^4) 0.62472
- C at infinite Reynolds number 0.60114
Checked against published worked examples from: ISO 5167-2:2003 (Reader-Harris/Gallagher equation); Caleb Bell, fluids (open-source Python library).
Details, formula, and sources
ScopeThe discharge coefficient C of a square-edge orifice plate from the beta ratio, the pipe Reynolds number, and the tap position (flange, corner, or D and D/2) by the Reader-Harris/Gallagher equation of ISO 5167-2, instead of assuming 0.61. A 4 in line (4.026 in ID) with a 2.013 in bore and flange taps at Re 200,000 gives C = 0.6049 and a flow coefficient of 0.6247. Re can be entered or computed from a liquid flow and viscosity, and the ISO limits of use are checked. Calibration governs.
Formula or tableC = 0.5961 + 0.0261 b^2 - 0.216 b^8 + 0.000521 (1e6 b/Re)^0.7 + (0.0188 + 0.0063 A) b^3.5 (1e6/Re)^0.3 + (0.043 + 0.080 e^-10L1 - 0.123 e^-7L1)(1 - 0.11 A) b^4/(1 - b^4) - 0.031 (M2 - 0.8 M2^1.1) b^1.3; A = (19000 b/Re)^0.8, M2 = 2 L2/(1 - b); corner L1 = L2 = 0, D and D/2 L1 = 1 and L2 = 0.47, flange L1 = L2 = 1 in/D; plus 0.011 (0.75 - b)(2.8 - D in) for D under 2.8 in; flow coefficient C/sqrt(1 - b^4); liquid Re = 4Q/(pi D nu).
Source and editionISO 5167-2:2003, Measurement of fluid flow by means of pressure differential devices, Part 2: Orifice plates (the Reader-Harris/Gallagher equation, also in ASME MFC-3M), cited by name.
Free accessThe equation is published in the standard and reproduced in the open-source fluids library (C_Reader_Harris_Gallagher), whose docstring value this matches to seven digits; the pipe, bore, taps and Reynolds number are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namespipe_id_in, bore_in, taps, reynolds_mode, reynolds_number, flow_gpm, viscosity_cst, discharge_coefficient, flow_coefficient, c_infinite_re
- Plate square-edge concentric orifice; quadrant-edge, conical-entrance and eccentric plates and venturis are not coveredISO 5167-2 scope
- Reynolds number entered, or from a liquid flow Q (gpm) and kinematic viscosity (cSt) as 4Q/(pi D nu); a gas's Re comes from its mass flowdefinition