Eshrak Kader
Excel is a popular and useful tool for analyzing data and solving complex equations. Now, one such case is the Colebrook equation which has to be solved numerically and this is where Excel becomes a very handy tool to perform such calculations effortlessly. Keeping this in mind, this article demonstrates 3 effective ways how to solve Colebrook equation in Excel.
Download Practice Workbook
You can download the practice workbook from the link below.
What Is Colebrook Equation?
In simple terms, the Colebrook equation shows the relationship between the Reynolds number, Pipe Roughness, and Diameter with the Friction factor of the pipe.
The variables of the Colebrook equation are as follows.
- Friction Factor, f
- Pipe Roughness, k
- Pipe Diameter, D
- Reynolds Number, Re
3 Ways to Solve Colebrook Equation in Excel
By now you’ve probably figured out that the Colebrook is an implicit equation because the friction factor term is present on both sides of the expression. Hence, this equation can be solved either numerically or through trial and error.
Now, let’s consider the dataset shown in the B4:D12 cells. Here, we have the distribution of the Pipe Roughness and the Reynolds Number for a fixed Pipe Diameter. So, without further delay let’s see each method individually.
Here, we have used Microsoft Excel 365 version, you may use any other version according to your convenience.
Method-1: Using Goal Seek Tool to Solve Colebrook Equation
Let’s start with the most popular method of solving the Colebrook equation in Excel. Yes, you’ve guessed it correctly! We’ll utilize Excel’s Goal Seek tool to solve the equation. So, just follow these steps below.
📌 Steps:
- At the very beginning, enter the left side of the Colebrook equation in the C9 cell.
=1/SQRT(B9)
Here, the B9 cell refers to the Friction Factor and is also the number argument of the SQRT function.
- Next, move to the D9 cell and type in the right side of the Colebrook expression. For your ease of use, you may copy the expression below.
=-2*LOG((D4/(3.7*D5))+(2.51/(D6*SQRT(B9))))
Here, the D4, D5, and D6 cells represent the Pipe Roughness, Pipe Diameter, and Reynolds Number respectively. Moreover, use Excel’s LOG function according to the equation.
- Then, navigate to the E9 cell and calculate the difference between the right side and the left side.
=D9-C9
In this formula, the C9 and D9 cells point to the LHS and RHS respectively.
- In turn, go to the Data tab >> click the What-If Analysis drop-down >> select the Goal Seek option.
Subsequently, this opens the Goal Seek wizard.
- Next, in the To value field type in 0 while for the By changing cell option select the B9 cell.
Finally, your output should look like the picture given below.
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Method-2: Utilizing Worksheet Iteration to Solve Colebrook Equation
For those of you who want to learn about more techniques, Excel has a nifty trick up its sleeve! Simply put, you can use the Worksheet Iteration feature of Excel to solve the Colebrook equation. In order to do this, we’ll rearrange the Colebrook equation as shown below. So, let’s see it in action.
📌 Steps:
- To begin with, click the File tab at the top left corner.
- Next, click the Options button at the bottom of the window.
This opens the Excel Options dialog box.
- Now, click the Formulas option >> insert a checkmark on the Enable iterative calculation option >> hit the OK button.
Here, you can set the Maximum Iterations to 500 and the Maximum Change to 0.0001.
- Secondly, rearrange the Colebrook equation as shown below and enter it into the D8 cell.
=1/(-2*LOG(D4/(D5*3.7) + 2.51/(D6*SQRT(D8+1E-300))))^2
In this expression, the D4, D5, D6, and D8 cells represent the Pipe Roughness, Pipe Diameter, Reynolds Number, and Friction Factor respectively.
📄Note: When Excel begins iterating, it sets the value in the D8 cell to zero. This would return #DIV/0! Error so to solve this we’ve added a small number (1E-300) which doesn’t affect the accuracy of the result.
- Following this, move to the D9 cell and enter the cell reference for the D8 cell.
=D8
Consequently, Excel performs the iterations and returns the correct result as shown in the image below.
Read More: How to Solve 2 Equations with 2 Unknowns in Excel (2 Examples)
Method-3: Applying VBA to Solve Colebrook Equation
Thus far, what we’ve done is nice, but there is a major problem i.e. each time we change the Friction Factor we’ll have to re-run the Goal Seek tool. However, we can automate this repetitive task using VBA. Now, allow me to demonstrate the process in the steps below.
📌 Step-01: Open Visual Basic Editor
- Firstly, navigate to the Developer tab >> click the Visual Basic button.
This opens the Visual Basic Editor in a new window.
📌 Step-02: Insert VBA Code
- Secondly, go to the Insert tab >> select Module.
For your ease of reference, you can copy the code from here and paste it into the window as shown below.
Sub Solve_Colebrook()
Static Computing As Boolean
If Round(Range("E9").Value, 3) <> 0 And Not Computing Then
Computing = True
Range("B9").Value = 0.01
Range("E9").GoalSeek goal:=0, ChangingCell:=Range("B9")
Computing = False
End If
End Sub
⚡ Code Breakdown:
Now, I will explain the VBA code for solving the Colebrook equation. Here, the code is divided into 2 sections.
- In the first portion, the sub-routine is given a name, here it is Solve_Colebrook().
- Next, define the variable Computing and assign Boolean data type.
- In the second potion, use the If statement to check if the value in the E9 cell is not equal to zero and not equal to Computing.
- Now, set the value in the B9 cell to 0.01 using the Range object.
- Finally, apply the Goal Seek method to determine the value of the B9 cell (Friction factor) which gives zero in the E9 (RHS – LHS) cell.
📌 Step-03: Running VBA Code
- Now, close the VBA window >> click the Macros button.
This opens the Macros dialog box.
- Following this, click the Run button.
Eventually, the results should look like the screenshot given below.
Read More: Solve Quadratic Equation in Excel VBA (with Quick Steps)
Practice Section
Here, we have provided a Practice section on the right side of each sheet so you can practice yourself. Please make sure to do it by yourself.
Conclusion
I hope all of the methods on how to solve Colebrook equation in Excel will now prompt you to apply them in your Excel spreadsheets more effectively. If you have any questions or feedback, please let me know in the comment section. Or you can check out our other articles related to Excel functions on this website.
