How to use this calculator
Enter the pipe and throat diameters, the fluid density and the discharge coefficient. Give the pressure drop from the inlet to the throat directly, or as a differential manometer reading with the gauge-fluid density.
Formulas
Flow rateQ = CdA2√(2Δp / (ρ(1 − β⁴))), β = D2/D1
ManometerΔp = (ρm − ρ)gΔh
Worked example
Water, D₁ = 100 mm, D₂ = 50 mm, mercury reading 200 mm, Cd = 0.98 (the default)
- Δp = (13 600 − 1000)(9.81)(0.2) = 24 721 Pa, β = 0.5.
- A₂ = π(0.05)²/4 = 0.0019635 m², so Qideal = 0.0019635√(2 × 24 721/(1000 × 0.9375)) = 0.01426 m³/s.
- Q = 0.98 × 0.01426 = 13.97 L/s.
Frequently asked questions
Why ρm − ρ?
The pipe fluid fills both legs above the gauge fluid, so its weight partly cancels; only the density difference over the reading counts.
Does the meter’s angle matter?
Not with a differential manometer: the elevation change is included automatically in the reading.