Colebrook-White Equation in Excel

The Colebrook-White equation is used to calculate the friction factor (f) in turbulent flow within pipes. The formula accounts for the effects of relative roughness and Reynolds number. The equation is implicit and requires iterative methods to solve for f.

Colebrook-White Equation

The Colebrook-White equation can be expressed as:

[ \frac{1}{\sqrt{f}} = -2 \log_{10} \left( \frac{\epsilon/D}{3.7} + \frac{5.74}{Re^{0.9}} \right) ]

Where:

• ( f ) = friction factor (dimensionless)
• ( \epsilon ) = roughness height of the pipe (meters)
• ( D ) = diameter of the pipe (meters)
• ( Re ) = Reynolds number (dimensionless)

Excel Implementation

Inputs Required

1. A1: Diameter of the pipe (D)
2. A2: Roughness height of the pipe (ε)
3. A3: Reynolds number (Re)

Excel Formula

To compute the friction factor (f) in cell A4, you can use an iterative approach with Excel’s Goal Seek or by implementing the following formula directly if you're using a helper cell for iterations.

Assuming f is in cell A5:

1. Initial estimate for f: Set A5 to a value, e.g., 0.02.
2. In A4, enter the following formula:

=1/(2*LOG10(A2/A1/3.7 + 5.74/(A3^0.9))^(-1))

Using Goal Seek

1. Set up the following equation in cell A4 without inserting a friction factor, e.g., use:

= 1/(2*LOG10((A2/A1)/3.7 + (5.74/(A3^0.9))))

2. Use Excel's Goal Seek feature:
   • Set cell A4 to value 1/(2 * LOG10(...)) using the value in A5.

Explanation of the Formula

• LOG10: Calculates the base-10 logarithm.
• 1/(...): Represents the left-hand side of the Colebrook-White equation, thus calculating the friction factor (f).
• The relative roughness ( \epsilon/D ) accounts for pipe surface texture, and ( Re ) encompasses the flow characteristics.

Practical Example

Assume:

• Diameter of the pipe (D) = 0.1 m
• Roughness height (ε) = 0.0002 m
• Reynolds number (Re) = 100000.

Step-by-Step Example

1. Input:
   • A1 = 0.1 (pipe diameter)
   • A2 = 0.0002 (roughness height)
   • A3 = 100000 (Reynolds number)
2. Initial Estimate:
   • A5 = 0.02 (initial guess for f)
3. Formula in A4:
   • Apply the provided formula to compute the friction factor iteratively until it converges.

Output

After applying the formula using Excel’s Goal Seek, the resulting friction factor (f) can be determined, yielding a usable value for further hydraulic calculations.

Conclusion

The Colebrook-White equation is critical for calculating friction in turbulent flow in pipes. Excel can facilitate this through iterative methods, allowing precise computations relevant in various engineering applications. For further proficiency in such calculations and overall data analysis, consider utilizing the Enterprise DNA Platform for comprehensive training and resources.