The venturi flow meter operates based on the principle of Bernoulli's equation and the conservation of energy to measure the flow rate of fluids in a pipe. Here's how it works:

1. Principle of Bernoulli's Equation:

   • Bernoulli's equation states that in a fluid flow system, the sum of the kinetic energy, potential energy, and pressure energy of the fluid remains constant along a streamline. Mathematically, it can be expressed as:
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• • P₁/ρ + V₁²/2 + gz₁ = P₂/ρ + V₂²/2 + gz₂

  • Where:
    • P₁ and P₂ are the pressures at points 1 and 2 along the streamline,
    • ρ is the fluid density,
    • V₁ and V₂ are the fluid velocities at points 1 and 2,
    • g is the gravitational acceleration, and
    • z₁ and z₂ are the elevations of points 1 and 2.

• Venturi Meter Design:

  • A venturi flow meter consists of a converging inlet section, a throat section with a reduced diameter, and a diverging outlet section.
  • The converging section of the venturi tube accelerates the flow velocity, resulting in a decrease in pressure according to Bernoulli's equation.
  • At the throat section, where the pipe diameter is smallest, the flow velocity reaches its maximum value, and the pressure reaches its lowest point due to the venturi effect.
  • In the diverging section, the flow velocity decreases as the pipe diameter increases, leading to a recovery of static pressure.

• Pressure Difference Measurement:

  • A differential pressure (DP) transmitter is installed upstream and downstream of the venturi meter to measure the pressure difference (ΔP) between the two points.
  • The pressure difference (ΔP) is proportional to the square of the flow rate (Q) according to Bernoulli's equation:
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• • ΔP = (P₁ - P₂) = ρ * V₂² / 2

  • The DP transmitter measures the pressure difference and converts it into an electrical signal proportional to the flow rate.

• Flow Rate Calculation:

  • The flow rate (Q) through the venturi meter can be calculated using the pressure difference (ΔP), fluid density (ρ), and other flow meter parameters, such as the venturi coefficient (Cv or Cd):
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4. • Q = Cv * A * sqrt(2 * ΔP / ρ)

   • Where:
     • Cv is the venturi coefficient,
     • A is the cross-sectional area of the throat section.

5. Advantages and Limitations:

   • Advantages:
     • Venturi flow meters offer high accuracy and repeatability over a wide range of flow rates.
     • They have lower permanent pressure losses compared to orifice plates.
     • They are less sensitive to variations in upstream flow conditions and offer better performance in non-ideal piping configurations.
   • Limitations:
     • Venturi meters are more expensive to install and require longer straight pipe lengths for proper installation compared to orifice plates.
     • They have a limited turndown ratio compared to other flow meter types such as ultrasonic meters.

In summary, venturi flow meters provide accurate and reliable flow measurement by utilizing the principle of Bernoulli's equation and the venturi effect to create a pressure difference proportional to the flow rate.