FRICTION_LAMINAR

Returns Darcy friction factor for laminar pipe flow from Reynolds number using the theoretical fully developed round-pipe relation.

The model is:

f_d = \frac{64}{Re}

This is the standard baseline expression for laminar internal flow and is typically applied for Re < 2040 in round pipes.

Excel Usage

=FRICTION_LAMINAR(Re)

• Re (float, required): Reynolds number, [-]

Returns (float): Darcy friction factor for laminar round-pipe flow [-]

Example 1: Typical laminar flow (Re = 128)

Inputs:

Re
128

Excel formula:

=FRICTION_LAMINAR(128)

Expected output:

0.5

Example 2: Very low Reynolds number (Re = 10)

Inputs:

Re
10

Excel formula:

=FRICTION_LAMINAR(10)

Expected output:

6.4

Example 3: Moderate laminar flow (Re = 500)

Inputs:

Re
500

Excel formula:

=FRICTION_LAMINAR(500)

Expected output:

0.128

Example 4: Near transition Reynolds number (Re = 2000)

Inputs:

Re
2000

Excel formula:

=FRICTION_LAMINAR(2000)

Expected output:

0.032

Python Code

Show Code

from fluids.friction import friction_laminar as fluids_friction_laminar

def friction_laminar(Re):
    """
    Calculate the Darcy friction factor for laminar flow using the theoretical solution fd = 64/Re.

    See: https://fluids.readthedocs.io/fluids.friction.html#fluids.friction.friction_laminar

    This example function is provided as-is without any representation of accuracy.

    Args:
        Re (float): Reynolds number, [-]

    Returns:
        float: Darcy friction factor for laminar round-pipe flow [-]
    """
    try:
      Re = float(Re)

      if Re <= 0:
        return "Error: Reynolds number must be positive."

      result = fluids_friction_laminar(Re=Re)

      if result != result:
        return "Error: Result is NaN."
      if result == float('inf') or result == float('-inf'):
        return "Error: Result is not finite."

      return float(result)
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number, [-]