About Orifice Flow Meter Calculator
The orifice flow meter calculator computes the flow rate through a concentric thin-plate orifice from the differential pressure measured across it, following the ISO 5167 metering standard. Enter the pipe internal diameter D, the orifice bore d (or the diameter ratio beta = d/D), the differential pressure dP, the fluid density and viscosity, and the discharge coefficient Cd.
An orifice plate creates a measurable pressure drop as flow contracts through the bore. The tool applies Q = (Cd / sqrt(1 - beta^4)) * (pi/4) d^2 * sqrt(2 dP / rho), where the term 1/sqrt(1 - beta^4) is the velocity-of-approach factor that corrects for the upstream pipe velocity. It returns the volumetric and mass flow, the pipe and throat velocities, and the throat Reynolds number used to confirm that the discharge coefficient is valid.
How It Works
- Choose whether to specify the orifice by its diameter ratio beta = d/D or by its bore diameter d, then enter the pipe diameter D.
- Enter the differential pressure dP across the orifice, the fluid density rho, the dynamic viscosity mu, and the discharge coefficient Cd (typically 0.60 to 0.62 for a sharp-edged orifice).
- The calculator forms beta, the velocity-of-approach factor E = 1/sqrt(1 - beta^4), and the throat area pi/4 * d^2, then evaluates Q = Cd * E * (pi/4) d^2 * sqrt(2 dP / rho).
- It derives the mass flow Q*rho, the pipe and throat velocities by continuity, and the throat Reynolds number, and plots flow against differential pressure.
Worked Example
A D = 0.1 m water pipe (rho = 1000 kg/m^3) carries an orifice with diameter ratio beta = 0.5, so the bore is d = 0.05 m. The differential pressure is dP = 5000 Pa and the discharge coefficient is Cd = 0.61. The velocity-of-approach factor is E = 1/sqrt(1 - 0.5^4) = 1/sqrt(0.9375) = 1.0328. The throat area is pi/4 * 0.05^2 = 0.0019635 m^2. The volumetric flow is Q = 0.61 * 1.0328 * 0.0019635 * sqrt(2*5000/1000) = 0.61 * 1.0328 * 0.0019635 * 3.1623 = 0.003912 m^3/s, giving a mass flow of Q*rho = 3.912 kg/s. The pipe velocity is Q / (pi/4 * 0.1^2) = 0.498 m/s.
Formulas
- Orifice flow equation (ISO 5167)
Q = (Cd / sqrt(1 - beta^4)) * (pi/4) * d^2 * sqrt(2 * dP / rho)- Diameter ratio and velocity-of-approach factor
beta = d / D, E = 1 / sqrt(1 - beta^4)- Mass flow and velocities
m_dot = Q * rho, V_pipe = Q / (pi/4 D^2), v_throat = Q / (pi/4 d^2)- Throat Reynolds number
Re_d = rho * v_throat * d / mu
Standards & References
- ISO 5167-1/-2 Measurement of fluid flow by pressure differential devices
- ASME MFC-3M orifice metering
- Miller, Flow Measurement Engineering Handbook
Frequently Asked Questions
What is the discharge coefficient Cd for an orifice plate?
The discharge coefficient accounts for the contraction of the jet (vena contracta) and frictional losses. For a sharp-edged concentric orifice it is typically about 0.60 to 0.62 and varies slowly with the diameter ratio beta and the throat Reynolds number. ISO 5167 gives the Reader-Harris/Gallagher equation for Cd; this tool lets you enter the value directly.
What is the velocity-of-approach factor and why is it needed?
The velocity-of-approach factor E = 1/sqrt(1 - beta^4) corrects the orifice equation for the kinetic energy the fluid already has in the upstream pipe. As the diameter ratio beta increases the upstream velocity becomes significant, so E grows above 1. For beta = 0.5 it is 1.033, and it rises steeply as beta approaches 1.
Why must the diameter ratio beta be less than 1?
Beta = d/D is the ratio of the orifice bore to the pipe diameter, so a physical orifice must be smaller than the pipe (beta < 1). As beta approaches 1 the velocity-of-approach factor 1/sqrt(1 - beta^4) tends to infinity, which is why ISO 5167 restricts beta to roughly 0.1 to 0.75 for accurate metering. The calculator rejects beta of 1 or greater.
Why does the calculator report the throat Reynolds number?
The discharge coefficient of an orifice is only valid above a minimum Reynolds number (ISO 5167 typically requires a pipe Reynolds number of at least a few thousand). Reporting the throat Reynolds number lets you confirm the flow is turbulent enough for the chosen Cd to apply; at very low Reynolds numbers Cd rises and the standard correlations no longer hold.