Assignment Fanning friction factor (f) is predicted for a given Reynold's number, Re, by the von Karman equation: = 4.0 log10(Re V7) - 0.4 For a given Re, we want the f which is the root of fanning(f, Re) = 4.0 - log10(Re (7) -0.4 - Use Matlab and the von Karman equation to: 1. Derive an equation that allows the Fanning friction factor (f) to be found for a given value of Reynolds Number (Re) via root finding. 2. Create a Matlab function that calculates the equation. It should receive values off and Re and return a value that will equal zero when the von Karman equation is satisfied. Note that this can be a separate function in its own M-file or an anonymous function created within the script file below. 3. Write a script file to execute the following solution steps Set the Reynolds number to 50,000. Use linspace to create an array of friction factors from .001 to.01. Call your function with the given Reynolds number and the array of friction factor values. Plot the resulting array as a function friction factor Turn on the grid Add a title and X and Y labels Capture the plot for insertion into a Word or other format document 4. Use fzero to find the value off for Re = 50000: Hint: use a initial guess of 0.004. 5. Add your name and the assignment number at the top of the document then insert the plot. Add either a screen shot or cut/paste of your function and script. Add your estimate of the root. Save the document to PDF format and submit to In Class 03 on Blackboard