Why is the Bernoulli theory not applicable for the Control Valve?

Bernoulli’s principle is a fundamental concept in fluid dynamics that states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy.

Bernoulli’s principle

The Bernoulli theory, while useful in many fluid flow applications, isn’t fully applicable to control valves due to several reasons:

  1. Viscosity: Bernoulli’s principle assumes an ideal fluid that is incompressible and has no viscosity. However, real-world fluids do have viscosity, which is a form of internal friction that resists fluid flow. When a fluid passes through a control valve, this friction plays a significant role and affects the pressure, velocity, and flow rate. This means that a control valve’s operation can’t be fully explained by Bernoulli’s principle alone.
  2. Energy Losses: Bernoulli’s principle assumes energy conservation in a flowing fluid without considering energy losses due to friction and turbulence, especially when the fluid passes through obstructions like a control valve. When fluid flows through a control valve, there’s significant turbulence and energy loss, leading to a drop in pressure that Bernoulli’s principle doesn’t account for.
  3. Changes in Flow Area: Bernoulli’s principle doesn’t account for changes in the cross-sectional area of a pipe, which is what happens in a control valve. The control valve works by changing the cross-sectional area available for the fluid flow, which can lead to an increase in velocity and a decrease in pressure. However, this pressure change doesn’t always follow Bernoulli’s principle due to turbulence and energy losses.
  4. Compressible Flow: Bernoulli’s principle is mainly applicable to incompressible flow. When gas goes through a control valve, especially at high pressure, the gas behaves compressibly, i.e., the volume of gas changes with pressure changes. This compressible nature of the gas does not comply with Bernoulli’s principle.

Bernoulli’s principle can give a basic understanding of some aspects of fluid dynamics, it doesn’t fully describe the more complex behavior of real-world fluids passing through control valves.