1. What is Displacement Thickness?

Displacement thickness is a concept in fluid dynamics that represents the distance by which the external streamlines are shifted due to the formation of a boundary layer. It quantifies how much the boundary layer has displaced the main flow.

2. How Does the Calculator Work?

The calculator uses the displacement thickness formula:

Where:

• \( \delta_d \) — Displacement thickness (m)
• \( \delta_{hx} \) — Hydrodynamic boundary layer thickness at distance X (m)

Explanation: The displacement thickness is calculated as one-third of the hydrodynamic boundary layer thickness, providing a measure of how much the boundary layer displaces the main flow.

3. Importance of Displacement Thickness Calculation

Details: Displacement thickness is crucial for understanding boundary layer effects in fluid flow, particularly in aerodynamics and hydrodynamics. It helps in calculating the effective shape of bodies in flow and is essential for accurate drag and lift calculations.

4. Using the Calculator

Tips: Enter the hydrodynamic boundary layer thickness in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of displacement thickness?
A: Displacement thickness represents the distance the external streamlines are displaced outward due to the boundary layer formation, affecting the effective shape of the body in the flow.

Q2: Why is displacement thickness exactly one-third of boundary layer thickness?
A: This relationship holds for laminar boundary layers with a parabolic velocity profile, which is a common approximation in fluid dynamics.

Q3: Does this formula apply to turbulent boundary layers?
A: No, this specific formula (δ_d = δ_hx/3) is typically valid for laminar boundary layers. Turbulent boundary layers have different displacement thickness relationships.

Q4: How is displacement thickness used in practical applications?
A: It's used in aircraft design, ship hull design, and any application where boundary layer effects on flow patterns need to be accounted for in calculations.

Q5: Can displacement thickness be measured directly?
A: While it's a theoretical concept, it can be derived from velocity profile measurements within the boundary layer using appropriate integration methods.