Estimate liquid flow through a venturi with a 4.000-inch actual pipe inside diameter and a 2.000-inch throat. Use a supplied discharge coefficient of 0.98 and inlet-to-throat differential pressure of 5 psi.
1. Calculator Inputs
Select the units below before entering the numbers. These are fixed benchmark inputs for checking the calculator.
| Calculator field | Value | Unit / setting |
|---|---|---|
| Solve for | Flow rate, Q | |
| Pipe inside diameter | 4 | in |
| Throat diameter | 2 | in |
| Fluid density | 62.4 | lbm/ft³ |
| Discharge coefficient, Cd | 0.98 | dimensionless |
| Inlet-to-throat differential pressure | 5 | psi |
2. Step-by-step Math
Convert geometry and properties
D = 4 × 0.0254 ≈ 0.102 m d = 2 × 0.0254 ≈ 0.0508 m β = d/D = 0.5 At = πd²/4 ≈ 0.00203 m² ρ = 62.4 × 0.45359237 / 0.3048³ = 999.552114535 kg/m³ ΔP = 5 × 6894.757293168 ≈ 34,500 Pa
The stated 4-inch pipe diameter is an actual bore. It does not mean NPS 4 Schedule 40.
Calculate liquid flow
Q = Cd At √[2ΔP / (ρ(1−β⁴))]
Q = 0.98 × 0.00202682991639
× √[2 × 34473.78646584 / (999.552114535 × 0.9375)]
Q = 0.017037839146 m³/s
Q = 61.336220925 m³/h ≈ 270 US gpmThe coefficient is an input. It has not been inferred from venturi geometry or calibration.
Check throat and pipe velocity
Vthroat = Q/At = 8.406151403 m/s Vpipe = Q/(πD²/4) = 2.101537851 m/s Vthroat / Vpipe = (D/d)² = 4
A throat with half the pipe diameter has one quarter of the area, so the average velocity is four times as high.
3. Compare Your Answers
Keep full precision during the calculation. The calculator may display fewer digits; compare answers rounded to three significant figures; retain unrounded intermediate values.
| Result | Expected answer | Your answer |
|---|---|---|
| Liquid flow | 61.3 m³/h | __________ |
| Flow in US units | 270 gpm | __________ |
| Beta ratio | 0.5 | __________ |
| Throat velocity | 8.41 m/s | __________ |
Second check
Select Differential pressure and enter 270.055256094 gpm with the same dimensions, density and Cd. The result returns to 5 psi. Next select Throat diameter with that flow and differential; the result should be 50.8 mm, or 2 inches.
4. Assumptions and Method
Single-phase incompressible flow with a specified Cd. The pressure differential is from inlet to throat, not the permanent downstream pressure loss. This example does not validate meter calibration, cavitation margin, gas expansion or a meter standard.
Equation definitions and implementation: Venturi Flow Calculator. See also calculation methodology and other worked examples.