Moody Chart Calculator Online

Calculate friction factors using the Colebrook-White equation with our interactive Moody diagram. Enter Reynolds number and relative roughness for accurate pipe flow calculations.

Friction Factor Calculator

Dimensionless number characterizing flow regime

Ratio of pipe roughness to diameter (dimensionless)

Quick Examples:

Interactive Moody Diagram

• Red point shows your calculated result

• Lines represent different relative roughness values

• Log-log scale for accurate representation

Understanding the Moody Chart and Friction Factor Calculations

What is a Moody Chart?

The Moody Chart, also known as the Moody Diagram, is a fundamental tool in fluid mechanics developed by Lewis Ferry Moody in 1944. This logarithmic graph provides a visual method to determine the Darcy friction factor (f) for pipe flow calculations. The chart plots the friction factor against the Reynolds number for various relative roughness values, making it an essential reference for engineers working with pipe flow systems.

The Colebrook-White Equation

The theoretical foundation of the Moody Chart is the Colebrook-White equation, which provides an implicit relationship for calculating the friction factor in turbulent flow:

1/√f = -2.0 × log₁₀((ε/D)/3.7 + 2.51/(Re√f))

Where f is the friction factor, ε/D is the relative roughness, and Re is the Reynolds number. Since this equation is implicit in f, it requires iterative numerical methods to solve, which our calculator handles automatically using the Newton-Raphson method.

Key Parameters Explained

Reynolds Number (Re)

The Reynolds number is a dimensionless parameter that characterizes the flow regime in a pipe. It is calculated as:

Re = ρVD/μ = VD/ν

Where ρ is fluid density, V is average velocity, D is pipe diameter, μ is dynamic viscosity, and ν is kinematic viscosity. Flow is generally considered laminar for Re < 2,300, transitional for 2,300 < Re < 4,000, and turbulent for Re > 4,000.

Relative Roughness (ε/D)

Relative roughness is the ratio of the absolute roughness (ε) of the pipe material to the pipe diameter (D). Common values include: drawn tubing (0.000005), commercial steel (0.00015), galvanized iron (0.0005), cast iron (0.00085), and concrete (0.001-0.01). This parameter significantly affects the friction factor in turbulent flow but has minimal impact in laminar flow.

Practical Applications

The friction factor calculated using the Moody Chart is essential for various engineering applications:

  • Pressure Drop Calculations: Using the Darcy-Weisbach equation: ΔP = f(L/D)(ρV²/2)
  • Pump Sizing: Determining required pump head for piping systems
  • Pipeline Design: Optimizing pipe diameter for given flow rates and pressure constraints
  • Energy Loss Analysis: Calculating frictional losses in fluid distribution systems
  • HVAC Systems: Designing ductwork and water distribution systems

Numerical Solution Method

Our calculator uses the Newton-Raphson iterative method to solve the Colebrook-White equation. The algorithm starts with an initial guess based on the smooth pipe approximation and iteratively refines the solution until convergence is achieved (typically within 3-5 iterations). For laminar flow (Re < 2,300), the exact solution f = 64/Re is used instead.

Worked Examples

Example 1: Water Flow in Commercial Steel Pipe

Given:

  • • Water at 20°C
  • • Velocity: 2 m/s
  • • Pipe diameter: 0.1 m
  • • Commercial steel pipe (ε = 0.000045 m)

Solution:

  • 1. Re = VD/ν = (2)(0.1)/(1.004×10⁻⁶) = 199,203
  • 2. ε/D = 0.000045/0.1 = 0.00045
  • 3. Using Colebrook-White: f = 0.0195

Example 2: Oil Flow in Smooth Pipe

Given:

  • • Oil (ν = 5×10⁻⁵ m²/s)
  • • Velocity: 1.5 m/s
  • • Pipe diameter: 0.05 m
  • • Smooth pipe (ε ≈ 0)

Solution:

  • 1. Re = VD/ν = (1.5)(0.05)/(5×10⁻⁵) = 1,500
  • 2. ε/D ≈ 0 (smooth pipe)
  • 3. Laminar flow (Re < 2,300): f = 64/Re = 0.0427

Frequently Asked Questions

What is a Moody Chart?

A Moody Chart (or Moody Diagram) is a graphical representation used in fluid mechanics to determine the friction factor for flow in pipes. It plots the friction factor against Reynolds number for various relative roughness values, providing a visual method to solve complex fluid flow problems.

How is the friction factor calculated?

The friction factor is calculated using the Colebrook-White equation: 1/√f = -2.0 × log₁₀((ε/D)/3.7 + 2.51/(Re√f)). This implicit equation is solved iteratively using numerical methods. For laminar flow (Re < 2,300), the simpler equation f = 64/Re is used.

What is the Reynolds number?

Reynolds number (Re) is a dimensionless quantity that characterizes the flow regime in a pipe. It's calculated as Re = ρVD/μ = VD/ν, where ρ is density, V is velocity, D is diameter, μ is dynamic viscosity, and ν is kinematic viscosity. It determines whether flow is laminar (Re < 2,300) or turbulent (Re > 4,000).

What is relative roughness?

Relative roughness (ε/D) is the ratio of the absolute roughness (ε) of the pipe material to the pipe diameter (D). It's a dimensionless parameter that significantly affects the friction factor in turbulent flow. Common values range from 0.000005 for drawn tubing to 0.01 for rough concrete pipes.

How accurate is this calculator?

Our calculator uses the standard Colebrook-White equation with iterative numerical methods, providing results accurate to within 0.1% of theoretical values. The algorithm typically converges within 3-5 iterations and handles the full range of Reynolds numbers and relative roughness values found in practical engineering applications.

Can I use this for gas flow calculations?

Yes, the Moody Chart and Colebrook-White equation apply to any Newtonian fluid, including gases, as long as the flow is incompressible or the Mach number is less than 0.3. For compressible gas flow at higher velocities, additional corrections may be needed.