π― Orifice Plate Flow Calculator (ISO 5167)
Calculate volume/mass flow rates or differential pressure drops across sharp-edged orifice plates per ISO 5167-2. Supports Corner, Flange, and D-D/2 tappings with iterative solver and design validation alerts.
β‘ Fortran 90 Engine
Double Precision (IEEE 754)
β ISO / ASME Validated
Tools
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Released
Jun 2026
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Hardware & Sizing Partner: Need to size a control valve or check ASME flange bolt torque for this line?
π Sizing Parameters
π Sizing Results
Mass Flow Rate ($\dot{m}$)
β
kg/s
Volume Flow Rate ($Q$)
β
mΒ³/h
Differential Pressure ($\Delta P$)
β
kPa
Discharge Coef ($C_d$)
β
ISO 5167-2
Expansibility ($\epsilon$)
β
Gas expansion
Reynolds Number ($Re_D$)
β
Pipe flow
Pressure Loss ($\Delta\omega$)
β
kPa
Compliance: ISO 5167 Check OK
All parameters fall within standard limits. Calculated results are validated.
ISO 5167 Orifice Plate Sizing:
β’ $\dot{m} = \frac{C_d \cdot \epsilon \cdot \frac{\pi}{4} d^2}{\sqrt{1 - \beta^4}} \sqrt{2 \cdot \rho_1 \cdot \Delta P}$ (Mass Flow)
β’ $C_d = f(Re_D, \beta, \text{tap type})$ β Reader-Harris/Gallagher (1998) Eq.
β’ $\epsilon = 1 - (0.351 + 0.256\beta^4 + 0.93\beta^8)[1 - (P_2/P_1)^{1/\kappa}]$ (for gases)
β’ $\beta = d/D$ (Beta Ratio)
β’ $\dot{m} = \frac{C_d \cdot \epsilon \cdot \frac{\pi}{4} d^2}{\sqrt{1 - \beta^4}} \sqrt{2 \cdot \rho_1 \cdot \Delta P}$ (Mass Flow)
β’ $C_d = f(Re_D, \beta, \text{tap type})$ β Reader-Harris/Gallagher (1998) Eq.
β’ $\epsilon = 1 - (0.351 + 0.256\beta^4 + 0.93\beta^8)[1 - (P_2/P_1)^{1/\kappa}]$ (for gases)
β’ $\beta = d/D$ (Beta Ratio)
π Calculation Methodology: ISO 5167 Differential Pressure Orifice Flowmeter
Mathematical Model & Theory
Orifice plate meters measure mass and volumetric flow rate by creating a differential pressure $\Delta P$ across a calibrated concentric bore with diameter ratio $\beta = d/D$:
$$Q = \frac{C_d}{\sqrt{1 - \beta^4}} \varepsilon \frac{\pi d^2}{4} \sqrt{\frac{2 \Delta P}{\rho}}, \quad \dot{m} = \rho Q, \quad \beta = \frac{d}{D}$$
$$C_d = \text{Reader-Harris/Gallagher (R-H/G) Equation (ISO 5167-2)}$$
Assumptions
- Fully developed turbulent velocity profile upstream of orifice.
- Subsonic expansion factor $ arepsilon pprox 1.0$ for liquids and small gas $\Delta P/P_1$.
Academic References
- ISO 5167-2:2003: Measurement of fluid flow by means of orifice plates.
- Miller, R. W.: Flow Measurement Engineering Handbook, McGraw-Hill.
Worked Engineering Example
Problem Statement:
Water ($\rho = 1000\text{ kg/m}^3$) flows in a pipe $D = 100\text{ mm}$ with orifice bore $d = 50\text{ mm}$ ($\beta = 0.50$, $C_d = 0.602$). The measured differential is $\Delta P = 25\text{ kPa}$. Calculate flow rate.
Step-by-step Solution:
1. Approach factor: $E = 1 / \sqrt{1 - 0.5^4} = 1 / \sqrt{0.9375} \approx 1.0328$.
2. Bore area: $A_d = \pi(0.05)^2/4 = 0.0019635\text{ m}^2$.
3. Velocity term: $\sqrt{2(25000)/1000} = \sqrt{50} \approx 7.071\text{ m/s}$.
4. $Q = 0.602 \times 1.0328 \times 0.0019635 \times 7.071 \approx 0.008636\text{ m}^3/\text{s} = 31.09\text{ m}^3/\text{h}$ ($518.2\text{ L/min}$).
Final Result:
Flow rate is $Q = \mathbf{31.09\text{ m}^3/h}$ ($\mathbf{8.64\text{ L/s}}$).
Water ($\rho = 1000\text{ kg/m}^3$) flows in a pipe $D = 100\text{ mm}$ with orifice bore $d = 50\text{ mm}$ ($\beta = 0.50$, $C_d = 0.602$). The measured differential is $\Delta P = 25\text{ kPa}$. Calculate flow rate.
Step-by-step Solution:
1. Approach factor: $E = 1 / \sqrt{1 - 0.5^4} = 1 / \sqrt{0.9375} \approx 1.0328$.
2. Bore area: $A_d = \pi(0.05)^2/4 = 0.0019635\text{ m}^2$.
3. Velocity term: $\sqrt{2(25000)/1000} = \sqrt{50} \approx 7.071\text{ m/s}$.
4. $Q = 0.602 \times 1.0328 \times 0.0019635 \times 7.071 \approx 0.008636\text{ m}^3/\text{s} = 31.09\text{ m}^3/\text{h}$ ($518.2\text{ L/min}$).
Final Result:
Flow rate is $Q = \mathbf{31.09\text{ m}^3/h}$ ($\mathbf{8.64\text{ L/s}}$).