Differential-Pressure Flow Meter (Orifice / Venturi)
Liquid flow through an orifice plate, venturi, or flow nozzle, from the differential pressure across it.
Example
You enter
- Pipe inside diameter (in) 4
- Bore / throat diameter (in) 2
- Differential pressure (psi) 1
- Discharge coefficient Cd (when entered; orifice 0.61, venturi 0.98) 0.61
- Fluid density (lb/ft3, water 62.4) 62.4
You get
- Flow rate 75.2 gpm
- Beta ratio (d/D) 0.5
Checked against published worked examples from: DP flow meter (larger line cross-check).
Details, formula, and sources
ScopeQ = Cd A2 sqrt(2 dP / (rho (1 - beta^4))), with beta = bore/pipe ID. Flow tracks the SQUARE ROOT of dP. Cd ~ 0.61 square-edge orifice, 0.98 venturi, 0.97 flow nozzle (editable) -- a venturi passes far more at the same dP and recovers most of the pressure. A 2 in bore in a 4 in water line at 1 psi (Cd 0.61) flows 75 gpm; the same at Cd 0.98 (venturi) flows 121 gpm. Enter dP in psi (1 psi = 27.7 in w.c.) and fluid density (water 62.4 lb/ft^3). Incompressible liquid only; a gas needs a separate expansion factor Y, and a precise Cd comes from ISO 5167 / the meter calibration. A field/sizing estimate; the calibrated meter governs.
Formula or tableQ = Cd A2 sqrt( 2 dP / (rho (1 - beta^4)) ); A2 = pi/4 d^2 (throat area); beta = d/D (bore/pipe-ID ratio); the 1 - beta^4 term is the velocity-of-approach factor. Incompressible liquid.
Source and editionThe differential-pressure primary-element (orifice / venturi / flow-nozzle) flow equation; ISO 5167 defines the precise discharge coefficient Cd and installation, but the Bernoulli equation itself is public physics, cited by name.
Free accessThe Bernoulli DP-flow equation is first-principles fluid mechanics; a typical Cd (0.61 orifice, 0.98 venturi, 0.97 nozzle) is editable and the meter's own calibration governs the exact value.
What governsEstimate. AHJ and licensed professional govern.
API field namespipe_id_in, bore_in, dp_psi, cd, fluid_density_lb_ft3, flow_gpm, beta_ratio
- DP-flow equation Q = Cd A2 sqrt(2 dP/(rho (1 - beta^4))); flow ~ sqrt(dP)Bernoulli / ISO 5167 primary elements
- Discharge coefficient Cd ~ 0.61 orifice, 0.98 venturi, 0.97 nozzle (editable); or, for a square-edge orifice (added 2026-10-09), computed by the ISO 5167-2 Reader-Harris/Gallagher equation for flange, corner, or D and D/2 taps, iterated with Re = 4Q/(pi D nu); calibration governsISO 5167-2; orifice-discharge-coefficient
- Scope incompressible liquid only; a gas needs an expansion factor Yscope of this tile