Engineering & Scientific
Venturi Meter Differential-Pressure Flow Rate & Beta^4 Velocity-of-Approach
Convert differential pressure dP across a converging Venturi tube (ISO 5167) into volumetric and mass flow rate using throat beta ratio d_2/d_1 and approach factor 1 / SQRT(1 - beta^4).
Why neglecting upstream kinetic energy (beta^4) understates Venturi flow rate
Combining incompressible continuity A_1 * V_1 = A_2 * V_2 (so V_1 = (d_2 / d_1)^2 * V_2 = beta^2 * V_2) with horizontal Bernoulli pressure drop dP = 0.5 * rho * (V_2^2 - V_1^2) yields ideal throat speed V_2 = SQRT((2 * dP) / (rho * (1 - beta^4))). Omitting the beta^4 upstream kinetic-energy term underpredicts flow by > 3.3% already at beta = 0.50 and > 15% at beta = 0.70!
Multiplying by throat area A_2 = (PI() / 4) * d_2^2 and ISO-5167 machined Venturi discharge coefficient C_d (~0.98–0.995) yields volumetric flow Q = C_d * A_2 * SQRT((2 * dP) / (rho * (1 - beta^4))) in m^3/s (multiply by 1,000 for L/s and by rho for kg/s mass flow).
| ISO-5167 Venturi Quantity | Formula | Meter (d1=0.20 m, d2=0.10 m, dP=30 kPa) |
|---|---|---|
| Diameter Ratio beta | d_2 / d_1 | 0.5000 |
| Velocity-of-Approach E_v | 1 / SQRT(1 - beta^4) | 1.0328 (1 - beta^4 = 0.9375) |
| Ideal Throat Speed | SQRT(2 * dP / (rho * (1 - beta^4))) | 8.00 m/s |
| Actual Volumetric Flow | C_d * (PI()/4 * d_2^2) * V_ideal * 1000 | 61.58 L/s (at C_d = 0.98) |
Velocity-of-Approach Factor 1 / SQRT(1 - beta^4) Formula
Guard d_2 >= d_1 ("INVALID_BETA") and compute 1 / SQRT(1 - (d_2 / d_1)^4).
=IF(B3 >= B2, "INVALID_BETA", ROUND(1 / SQRT(1 - ((B3 / B2) ^ 4)), 4))ISO-5167 Volumetric Flow Rate Formula (L/s)
Evaluate throat area, beta^4 denominator, and square-root pressure drop inside LET and convert m^3/s to L/s.
=IF(B3 >= B2, "INVALID_BETA", LET(b_rat, B3 / B2, area_th, (PI() / 4) * (B3 ^ 2), v_th, SQRT((2 * MAX(0, B4)) / (B5 * (1 - (b_rat ^ 4)))), ROUND(B6 * area_th * v_th * 1000, 2)))Try the example
Use the original values or change them to test your understanding.