Vortex Flowmeters

Overview

Engineering reference data for Vortex Flowmeters in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Operating Principle

Vortex flowmeters operate by placing a bluff body (shedding bar) in the flow stream. As fluid passes the bluff body, alternating low-pressure vortices are shed from either side, creating a oscillatory pattern known as the von Kármán vortex street. The frequency of this vortex shedding is directly proportional to the fluid velocity.

Key Formula

The core operational principle is governed by the Strouhal equation: $f = St \cdot \frac{V}{d}$ where:

• $f$ is the vortex shedding frequency (Hz)
• $St$ is the Strouhal number (dimensionless)
• $V$ is the average fluid velocity (m/s)
• $d$ is the characteristic width of the bluff body (m)

The Strouhal number ($St$) is approximately constant (typically 0.21) for a wide range of Reynolds numbers, making the frequency a reliable velocity indicator.

Advantages and Limitations

Advantages:

• No moving parts, resulting in high reliability and low maintenance
• Suitable for a wide variety of fluids (liquids, gases, and steam)
• Linear relationship between frequency and flow velocity
• Wide turndown ratio (typically 10:1 to 20:1)

Limitations:

• Requires a minimum Reynolds number (typically > 20,000) for proper vortex shedding
• Sensitive to vibration and flow profile disturbances
• Minimum pipe velocity required to generate a measurable vortex signal
• Not suitable for very low-density fluids or highly viscous liquids

References

• Original Source