Boundary-Layer Momentum Thickness using Reynolds Number at Transition Point Calculator

Formula Used:

\[ \theta_t = \frac{Re \times \mu_e}{u_e \times \rho_e} \]

Reynolds Number (Re):

Static Viscosity (μe):

Pa·s

Static Velocity (ue):

m/s

Static Density (ρe):

kg/m³

Boundary-Layer Momentum Thickness (θt):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Boundary-Layer Momentum Thickness?

Boundary-layer momentum thickness is a key parameter in fluid dynamics that quantifies the momentum deficit in the boundary layer due to viscous effects. It's particularly important for analyzing transition points in boundary layer flow.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta_t = \frac{Re \times \mu_e}{u_e \times \rho_e} \]

Where:

\( \theta_t \) — Boundary-layer momentum thickness (m)
\( Re \) — Reynolds Number
\( \mu_e \) — Static Viscosity (Pa·s)
\( u_e \) — Static Velocity (m/s)
\( \rho_e \) — Static Density (kg/m³)

Explanation: This formula relates the momentum thickness to the Reynolds number and fluid properties, providing insight into boundary layer characteristics at transition points.

3. Importance of Momentum Thickness Calculation

Details: Accurate calculation of momentum thickness is crucial for predicting flow separation, transition from laminar to turbulent flow, and designing efficient aerodynamic surfaces and fluid systems.

4. Using the Calculator

Tips: Enter Reynolds number, static viscosity in Pa·s, static velocity in m/s, and static density in kg/m³. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of momentum thickness?
A: Momentum thickness represents the distance by which the boundary would have to be displaced to compensate for the momentum reduction due to boundary layer formation.

Q2: How does momentum thickness relate to boundary layer transition?
A: Momentum thickness is used in transition prediction criteria and helps determine when laminar flow becomes unstable and transitions to turbulent flow.

Q3: What are typical values of momentum thickness?
A: Momentum thickness values are typically very small compared to boundary layer thickness, often in the millimeter or sub-millimeter range for many engineering applications.

Q4: How does momentum thickness compare to displacement thickness?
A: While displacement thickness accounts for mass flow deficit, momentum thickness accounts for momentum deficit. Momentum thickness is usually smaller than displacement thickness.

Q5: What factors affect momentum thickness at transition?
A: Momentum thickness at transition is influenced by Reynolds number, pressure gradient, surface roughness, and flow disturbances in the free stream.