Pipe Capacity Calculator Colebrook White

Colebrook-White Equation:

\[ \frac{1}{\sqrt{f}} = -2 \log_{10} \left( \frac{\varepsilon/D}{3.7} + \frac{2.51}{Re \sqrt{f}} \right) \]

Roughness (ε):

Diameter (D):

Reynolds Number (Re):

Head Loss (Δh):

Length (L):

Flow Rate (Q):

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1. What is the Colebrook-White Equation?

The Colebrook-White equation is used to calculate the friction factor for turbulent flow in pipes. It provides a relationship between the friction factor, pipe roughness, diameter, and Reynolds number, allowing for accurate flow rate calculations in piping systems.

2. How Does the Calculator Work?

The calculator uses the Colebrook-White equation:

\[ \frac{1}{\sqrt{f}} = -2 \log_{10} \left( \frac{\varepsilon/D}{3.7} + \frac{2.51}{Re \sqrt{f}} \right) \]

And the flow rate equation:

\[ Q = A \sqrt{\frac{2g \Delta h}{f \frac{L}{D}}} \]

Where:

\( f \) — Friction factor (dimensionless)
\( \varepsilon \) — Pipe roughness (m)
\( D \) — Pipe diameter (m)
\( Re \) — Reynolds number (dimensionless)
\( Q \) — Flow rate (m³/s)
\( A \) — Cross-sectional area (m²)
\( g \) — Gravity acceleration (9.81 m/s²)
\( \Delta h \) — Head loss (m)
\( L \) — Pipe length (m)

3. Importance of Pipe Flow Calculation

Details: Accurate pipe flow calculations are essential for designing efficient piping systems, determining pump requirements, and ensuring proper fluid transport in various engineering applications including water supply, oil and gas pipelines, and industrial processes.

4. Using the Calculator

Tips: Enter pipe roughness in meters, diameter in meters, Reynolds number, head loss in meters, and length in meters. All values must be positive. The calculator uses an iterative method to solve the implicit Colebrook-White equation.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of validity for the Colebrook-White equation?
A: The equation is valid for turbulent flow (Re > 4000) and provides accurate results for both smooth and rough pipes.

Q2: How is the friction factor calculated iteratively?
A: The calculator uses an initial guess and iteratively refines the solution until convergence is achieved within a specified tolerance.

Q3: What are typical roughness values for different pipe materials?
A: Smooth pipes (glass, plastic): 0.0015 mm, Steel pipes: 0.045 mm, Concrete pipes: 0.3-3.0 mm, depending on condition.

Q4: Can this calculator be used for laminar flow?
A: No, the Colebrook-White equation is specifically for turbulent flow. For laminar flow (Re < 2000), use the Hagen-Poiseuille equation.

Q5: What is the significance of the Reynolds number?
A: The Reynolds number determines whether flow is laminar or turbulent and affects the friction factor calculation in the Colebrook-White equation.