What is head loss due to sudden expansion?

Short Answer:

Head loss due to sudden expansion occurs when a fluid flows from a smaller diameter pipe to a larger diameter pipe, causing a sudden reduction in velocity. This rapid change in flow velocity leads to turbulence, eddies, and flow separation in the expanded section of the pipe, resulting in a loss of energy or head.

This loss is caused by the conversion of kinetic energy into heat and turbulence instead of pressure recovery. The head loss depends on the difference in velocities of the fluid in both pipes and can be calculated using a standard formula derived from Bernoulli’s equation and continuity principle.

Detailed Explanation:

Head Loss Due to Sudden Expansion

When a fluid flowing through a pipeline encounters a sudden increase in cross-sectional area, the velocity of the fluid decreases abruptly. According to the principle of continuity, the product of velocity and area must remain constant, so as the pipe diameter increases, the velocity drops. However, this sudden expansion does not allow the fluid to adjust smoothly, causing flow separation and turbulent eddies at the junction of the expansion.

This disturbance results in the loss of mechanical energy of the fluid in the form of turbulence and heat, which is termed as head loss due to sudden expansion. It is one of the most common types of minor losses in fluid systems and occurs in pipelines, diffusers, and expansion joints.

The head loss represents the reduction in total head (or energy) between the smaller and larger section of the pipe, and it can be determined using Bernoulli’s equation and continuity principle.

Derivation of Head Loss Formula

Let:

  •  = cross-sectional areas of smaller and larger pipes respectively,
  •  = velocities of fluid in the smaller and larger pipes,
  •  = head loss due to sudden expansion,
  •  = pressures in smaller and larger sections,
  •  = density of the fluid,
  •  = acceleration due to gravity.

Step 1: Applying Bernoulli’s Equation Between Sections 1 and 2

Rearranging gives the expression for head loss:

Step 2: Pressure Difference Between the Two Sections

The pressure difference  is obtained using the momentum principle applied to the control volume between the two sections:

Substituting , we can simplify and rearrange to find:

Step 3: Substituting into Bernoulli’s Equation

Substitute this expression into the Bernoulli equation to obtain:

Simplifying further gives:

Final Expression for Head Loss

Where:

  •  = head loss due to sudden expansion (m),
  •  = velocity of fluid in smaller pipe (m/s),
  •  = velocity of fluid in larger pipe (m/s),
  •  = acceleration due to gravity (9.81 m/s²).

Explanation of Flow Behavior

When fluid flows from a smaller to a larger pipe, it does not immediately fill the new cross-section uniformly. The high-velocity jet entering the larger pipe expands gradually, leaving recirculation zones along the pipe wall.

These zones consist of eddies and vortices that cause:

  1. Flow separation — the fluid near the wall moves backward due to pressure recovery.
  2. Turbulence — irregular and chaotic flow patterns absorb kinetic energy.
  3. Pressure fluctuations — energy is dissipated as heat.

As a result, part of the fluid’s kinetic energy is lost, and only a portion of it is converted into pressure energy. The rest is wasted as turbulence.

Factors Affecting Head Loss Due to Sudden Expansion

  1. Difference in Pipe Diameters:
    • Greater difference between diameters leads to higher velocity change and more turbulence, increasing head loss.
  2. Flow Velocity:
    • Since loss depends on the square of velocity difference, higher inlet velocity results in larger head loss.
  3. Fluid Density and Viscosity:
    • Denser and more viscous fluids have higher energy dissipation rates.
  4. Expansion Geometry:
    • A perfectly sudden expansion causes maximum loss, while a gradual or conical expansion reduces turbulence and minimizes energy loss.

Numerical Example

Given:

  • Velocity in small pipe
  • Velocity in large pipe

To Find:

 

Hence, the head loss due to sudden expansion is 0.204 m of fluid head.

Practical Applications

  1. Piping Systems:
    Engineers consider sudden expansion losses while designing pipelines for water, oil, or gas transport.
  2. Hydraulic Machines:
    Expansion losses occur at diffuser exits in pumps and turbines, where velocity reduction is required.
  3. Energy Loss Analysis:
    Used to calculate efficiency and pressure recovery in flow systems.
  4. HVAC and Ventilation Systems:
    Air ducts are designed to minimize sudden expansions to reduce noise and power losses.

Methods to Reduce Head Loss Due to Sudden Expansion

  1. Use Gradual Expansions (Diffusers):
    • Smooth and gradual transitions reduce turbulence and allow better pressure recovery.
  2. Streamlined Joints:
    • Well-designed joints and connectors minimize energy loss.
  3. Optimized Flow Velocity:
    • Reducing high-velocity differences helps decrease loss.
  4. Smooth Pipe Interiors:
    • Reduces wall friction and helps maintain laminar flow transitions.
Conclusion

Head loss due to sudden expansion occurs when fluid flow suddenly moves from a smaller to a larger pipe, causing turbulence and energy dissipation. It results from the conversion of kinetic energy into turbulence and heat instead of useful pressure energy. The loss can be determined using the formula . Minimizing this loss is important for efficient fluid system design, which can be achieved through smooth transitions, diffusers, and proper flow control.