Fluid

density (ρ):
dynamic viscosity (μ):
kinematic viscosity (ν):
pipe diameter (D)
0.510.0
velocity (V)
1500
pipe flow cross-section
Reynolds number (Re)
dimensionless
Re = ρ · V · D μ = V · D ν

Thresholds:

  • Re < 2000: laminar flow (viscous forces dominate)
  • 2000 ≤ Re ≤ 4000: transitional flow
  • Re > 4000: turbulent flow (inertial forces dominate)

Directions

This simulation calculates the Reynolds number for flow through a pipe and shows the corresponding flow regime.

  • Use the fluid drop-down menu to select a fluid. Its density, dynamic viscosity, and kinematic viscosity are displayed below the menu.
  • Use the pipe diameter and velocity sliders to change the pipe diameter and the average fluid velocity.
  • The Reynolds number is calculated from these values, and the flow regime (laminar, transitional, or turbulent) is displayed in the badge above the figure.
  • The animation shows the flow in a pipe cross-section. For laminar flow, the streamlines are straight and the fluid moves fastest at the center of the pipe and slowest near the walls (parabolic velocity profile). As the Reynolds number increases above 2,000, the streamlines become unstable, and above 4,000 the flow is chaotic and well-mixed.
  • Click the Guided inquiry button to download a worksheet with activities that use this simulation.

Details

The Reynolds number is a dimensionless number that represents the ratio of inertial forces to viscous forces:

\[ Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu}, \]

where the kinematic viscosity is

\[ \nu = \frac{\mu}{\rho}. \]

For flow in a pipe:

  • \( Re < 2000 \): laminar flow
  • \( 2000 \le Re \le 4000 \): transitional flow
  • \( Re > 4000 \): turbulent flow

In laminar flow, the velocity profile is parabolic:

\[ v(r) = v_{max}\left[1 - \left(\frac{r}{R}\right)^2\right], \]

so the fluid velocity is zero at the pipe wall (the no-slip condition) and maximum at the center.

Symbols (CGS units):

  • \( \rho \) = fluid density (g/cm\(^3\))
  • \( \mu \) = dynamic viscosity (P = g/[cm s])
  • \( \nu \) = kinematic viscosity (St = cm\(^2\)/s)
  • \( V \) = average fluid velocity (cm/s)
  • \( D \) = pipe diameter (cm)
  • \( r \) = radial distance from the pipe center (cm)
  • \( R \) = pipe radius (cm)

About

This simulation was generated by Professor David L. Silverstein and Dr. Loyal Murphy of the University of Mississippi using Google Gemini. It was modified for LearnChemE using Claude AI.