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 (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
Details, formula, and sources
Q = 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.
Q = 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.
The 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.
The 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.
Estimate. AHJ and licensed professional govern.
Field names used by the API: pipe_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); precise Cd from ISO 5167 / calibrationISO 5167
- Scope incompressible liquid only; a gas needs an expansion factor Yscope of this tile