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Nozzle Flow Rate Calculator

Reviewed by the CalculatorHub team, edited by James Graham. Based on ISO 5167 differential pressure flowmeter formula. Last verified 14 June 2026.

This calculator computes the volumetric and mass flow rate through an orifice, nozzle, or Venturi meter using the ISO 5167 standard differential pressure flow equation. Enter the throat diameter, upstream pipe diameter, differential pressure, fluid density, and discharge coefficient. The calculator returns flow velocity at the throat, volumetric flow rate, and mass flow rate.

Nozzle or orifice throat (minimum) diameter
Internal diameter of the upstream pipe
Pressure difference between upstream tap and throat tap
Water at 20 C: 998 kg/m3. Air at standard conditions: 1.225 kg/m3.
Per ISO 5167. Use calibrated value if available.
0.50
-- m/s
-- L/s
-- kg/s

Nozzle flow formula (ISO 5167)

Q = Cd / sqrt(1 - beta4) × Athroat × sqrt(2 × dP / rho)
beta = d / D
Athroat = pi × d2 / 4

Where: Cd = discharge coefficient, beta = diameter ratio d/D, A = throat area (m^2), dP = differential pressure (Pa), rho = fluid density (kg/m^3). The term 1/sqrt(1 - beta^4) is the velocity of approach factor (E), which accounts for the kinetic energy in the upstream pipe.

Selecting a meter type

  • Sharp-edged orifice: lowest cost, simplest to install, highest permanent pressure loss (typically 60 to 80% of dP).
  • ASME/ISO long-radius nozzle: lower pressure loss than orifice (~30% of dP), better wear resistance, suitable for high velocity steam and water.
  • Venturi tube: lowest permanent pressure loss (~10 to 20% of dP), highest cost, requires more straight pipe upstream.
  • All types require a minimum of 10D to 30D of straight upstream pipe per ISO 5167.

Nozzle flow calculator: frequently asked questions

What is the nozzle flow equation?

The volumetric flow rate through a nozzle is Q = Cd * A * sqrt(2 * dP / rho), where Cd is the discharge coefficient, A is the throat cross-sectional area (m^2), dP is the differential pressure across the nozzle (Pa), and rho is the fluid density (kg/m^3). The mass flow rate is m_dot = rho * Q.

What are typical discharge coefficients?

For an ASME long-radius flow nozzle (per ISO 5167-3), Cd is approximately 0.98 to 0.99 at high Reynolds numbers (Re > 10^6). For a sharp-edged orifice, Cd is approximately 0.60 to 0.65. For a Venturi meter, Cd is approximately 0.98. A sharp-edged orifice has higher pressure loss but simpler construction.

What is the beta ratio?

The beta ratio (beta = d/D) is the ratio of the throat diameter d to the upstream pipe diameter D. ISO 5167 specifies valid beta ratios of 0.1 to 0.75 for orifice plates. Higher beta ratios produce a smaller differential pressure for the same flow, reducing measurement sensitivity but also reducing permanent pressure loss.

How does fluid compressibility affect the result?

For gases, an expansion factor Y (or epsilon) must be applied: Q = Cd * Y * A * sqrt(2 * dP / rho_1), where rho_1 is the upstream density. For pressure ratios dP/P1 less than 0.1 (low Mach number), Y is close to 1.0 and can often be ignored for preliminary calculations. ISO 5167 provides detailed expansion factor equations.

What ISO standard governs differential pressure flowmeters?

ISO 5167 (Parts 1 to 5) covers measurement of fluid flow using differential pressure devices. Part 1 covers general principles and requirements. Part 2 covers orifice plates. Part 3 covers nozzles and Venturi nozzles. Part 4 covers Venturi tubes. This calculator uses the basic formula from ISO 5167-1.

Official sources

  • ISO 5167-1:2003 Measurement of fluid flow using differential pressure devices: ISO 5167-1.
  • ISO 5167-3:2003 Nozzles and Venturi nozzles: ISO 5167-3.

Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.