Current position >About Us
Venturi Meter Working Principle: Bernoulli Fluid Dynamics and Pressure Drop Calculations
Quick Answer: A Venturi meter measures flow by reducing the pipe cross section at a throat and reading the pressure difference between the inlet and the throat. The differential pressure follows the Bernoulli equation. You can calculate the flow rate from pipe size, throat size, fluid density, and discharge coefficient.
Silver Automation Instruments supplies differential pressure transmitters and industrial flow meters for these calculations and installations. We work with water plants, oil and gas operators, chemical batch sites, and food processors across Southeast Asia, Oceania, Latin America, the Middle East, and Africa.
How a Venturi Meter Works
Think of a Venturi meter as a pipe section with three zones. The inlet zone matches the main pipe diameter. The middle zone narrows to a smaller diameter called the throat. After the throat, a diffuser cone returns the pipe to the original diameter.
Fluid enters at the inlet at velocity v1 and pressure P1. At the throat, the velocity increases because the same mass flow passes through a smaller area. The pressure at the throat is P2. P2 is lower than P1. This pressure difference is the differential pressure that a DP transmitter measures.
In practice, the Venturi meter is common on large water and steam lines where low permanent pressure loss matters. We have seen this on customer sites many times, especially in desalination plants and district cooling systems.
Bernoulli Equation in a Venturi Meter
For a horizontal pipe with no pump or turbine between the inlet and throat, the Bernoulli equation simplifies to:
P1 + 0.5 ρ v12 = P2 + 0.5 ρ v22
Here ρ is the fluid density in kg/m³. P1 and P2 are static pressures in Pa. v1 and v2 are average velocities in m/s.
The continuity equation keeps mass flow constant:
A1 v1 = A2 v2
A1 is the inlet cross sectional area and A2 is the throat cross sectional area. Combine the two equations and you get the Venturi flow formula. This is not a marketing claim. It is basic fluid dynamics that has been in use since the 1880s.
Pressure Drop Calculation Example
Here is a practical example. A water line has DN100 inlet diameter and a Venturi throat diameter of 50 mm. Water density is 998 kg/m³. A differential pressure transmitter reads 15 kPa between inlet and throat. The beta ratio β is 50 divided by 100, so β = 0.5.
A1 = π × 0.12 / 4 = 0.007854 m². A2 = π × 0.052 / 4 = 0.001963 m². The term sqrt(1 - β4) equals sqrt(1 - 0.0625) = 0.968. The term sqrt(2 × ΔP / ρ) equals sqrt(2 × 15000 / 998) = 5.48. If discharge coefficient C is 0.98, Q = 0.98 × 0.001963 / 0.968 × 5.48 = 0.0109 m³/s. That equals about 39.2 m³/h.
This is the working equation for an incompressible fluid. For gas or steam, you add an expansion factor Y. Most engineers skip the full derivation and go straight to ISO 5167 tables or a flow computer.
Flow Rate Formula and Discharge Coefficient
The full formula for incompressible flow is:
Q = C × A2 / sqrt(1 - β4) × sqrt(2 × ΔP / ρ)
Q is volumetric flow rate in m³/s. ΔP is the differential pressure in Pa. ρ is density in kg/m³. β is the throat diameter divided by the pipe diameter. C is the discharge coefficient.
C corrects for friction and flow contraction. For a machined or cast Venturi tube, C is often between 0.95 and 0.99. You cannot assume C is 1.0. A small change in C shifts the calculated flow by the same percentage.
For compressible flow such as natural gas, steam, or compressed air, use:
Q = C × Y × A2 / sqrt(1 - β4) × sqrt(2 × ΔP / ρ)
Y is the expansion factor. Y depends on the isentropic exponent, beta ratio, and pressure ratio. ISO 5167 gives the calculation path.