![]() By setting the objective to a target value of zero, Excel will iterate on the value of the friction coefficient. If the value of f is contained in a cell, Goal Seek automatically adjusts that value until an objective is met in another cell. In Microsoft Excel, the Colebrook equation can be solved using Goal Seek. The video below shows how to use the solver function on a graphing calculator to solve an equation. Using this functionality, you can enter the equation into your calculator with friction factor as a variable, and solve for f. Most graphing calculators have built-in capability to solve equations. How to Solve the Colebrook Equation by Calculator On the fourth iteration, the friction factor guess matches the friction factor result to 3 decimal places, therefore 0.0378 is a reasonable approximation of the friction factor. ![]() The table below shows the progression of iterations: Iteration Number The process above is continued until there is an approximate match between the guess value of f and the calculated value. Step 6: Repeat iteration until the guess value of f matches the calculated value Step 5: Use the new value of f in the right-hand side of the equation and recalculate Since the calculated value of f does not match the guess value of f, we need to continue iteration. Step 4: Check the accuracy of the solution Input the values for ε, Dh, and Re along with the guess value for f and calculate the result: Step 3: Solve the right-hand side of the equation Since the values of f range from 0.01 to 0.1, choose a value of 0.05 which is approximately the mean value of f. Step 1: Rearrange the Colebrook equation into the form: Step 2: Choose a guess value for f Calculate the Darcy friction factor.īecause the Reynolds number is greater than 4000 the flow in the pipe is turbulent, so the Colebrook equation can be used to calculate the pipe friction factor. Water is flowing through a pipe with a roughness height of 0.00005 meters, a hydraulic diameter of 0.025 meters. How to Solve the Colebrook Equation by Hand Therefore, iteration is required to solve the Colebrook equation. ![]() ![]() That means there is no way to arrange the equation to get the Darcy friction factor on one side of the equal sign. The Colebrook equation is an implicit equation. The above calculator uses the Haaland equation, an explicit approximation of the Colebrook equation, to calculate the friction factor. ![]()
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