Engineering
Bernoulli's Equation & Venturi Flowmeter differential-pressure formula
Calculate volumetric flow rate from Venturi throat pressure drop via Q = Cd * A2 * SQRT(2 * dP / (rho * (1 - (A2/A1)^2))) and throat velocity V2 = Q / A2.
Convert differential pressure dP across a pipe constriction into flow rate Q!
For steady incompressible flow with negligible elevation difference, combine continuity with ideal Bernoulli pressure and velocity terms. The throat area must be positive and smaller than the upstream pipe area. Differential pressure is upstream static pressure minus throat static pressure, in pascals.
The discharge coefficient corrects the ideal calculation empirically; 0.98 is an example input, not a universal constant. Use a coefficient calibrated for the geometry and flow regime. Compressible flow, cavitation, significant elevation differences and other installation effects need additional treatment.
Here A2/A1 is an area ratio. If using diameter ratio beta instead, (A2/A1)² equals beta⁴. Density is kg/m³ and area is m². A zero measured pressure difference returns zero in this idealized model; sensor resolution and offsets are not modeled.
| Venturi Parameter | Cell | Water Line Example | Fluid Result |
|---|---|---|---|
| Pipe Area A1 & Throat Area A2 | B2 = 0.02 m^2, B3 = 0.005 m^2 | Area ratio A2/A1 = 0.25 | Beta^4 = (0.25)^2 = 0.0625 |
| Pressure Drop dP & Density rho | B4 = 15,000 Pa, B5 = 1,000 kg/m^3 | 15 kPa differential across water | 2*dP / (rho*(1-0.0625)) = 32.00 |
| Discharge Coefficient Cd | B6 = 0.98 | Smooth converging nozzle | Ideal SQRT(32) = 5.6569 m/s |
| Flow Rate Q & Liters/sec | Venturi Equation | Q = 0.02772 m^3/s | 27.72 L/s (Throat V2 = 5.54 m/s) |
Venturi volumetric flow rate Q (m^3/s)
Multiply m^3/s by 1,000 to report industrial flow in Liters per second (27.72 L/s).
=IF(OR(COUNT(B2:B6)<>5,B2<=0,B3<=0,B3>=B2,B4<0,B5<=0,B6<=0,B6>1),"Invalid inputs",ROUND(B6 * B3 * SQRT((2 * B4) / (B5 * (1 - (B3 / B2) ^ 2))), 5))Flow in Liters per second (L/s) & zero-flow boundary
When differential pressure dP = 0 Pa, flow rate cleanly evaluates to 0.
=IF(OR(COUNT(B2:B6)<>5,B2<=0,B3<=0,B3>=B2,B4<0,B5<=0,B6<=0,B6>1),"Invalid inputs",ROUND(1000 * B6 * B3 * SQRT((2 * B4) / (B5 * (1 - (B3 / B2) ^ 2))), 2))Try the example
Use the original values or change them to test your understanding.