This equation has not been solved since 1930 when it was made.  The equation is for engineers to design pipes. But I want lots of folks to learn the equation because they will learn the easy and true solution because of the Log function.

There are two numbers that are needed for engineers.  
Rr is between 0.00004 and 0.05
Re is between 2,500 and 10,000,000

The solution is to solve the f.

Her is the equation  1/sqrt(f) = -2*Log(Rr/3.7 +2.51/(Re*sqrt(f)))

But the equation can be changed to 1/sqrt(f) = -2*Log(Rr/3.7 +2.51/Re*1/sqrt(f)) and then change the 1/sqrt(f) to X and solve for the X.   So the equation is            X = -2*Log(Rr/3.7 +2.51/Re*X)

The easy solution is to Guess (about 1 to 10) and X in a cell and below it type = -2*Log(Rr/3.7 +2.51/Re*X), but enter the Rr and Re numbers but for the X, just point to the Guess X.  Then format the equation to about 16 digits and then copy that equation to about 20 cells below, and the X will be using the previous cell that was the solving of the next X.  Then before the 20th cell the solution for X will stop changing. You can change the Guess X and the last solution will not not change.

The to compute the f it is =1/X/X, (just below to 20th cell) and for the X just point to the bottom cell. You can change the Rr and Re in the cell below the Guessed X and copy the new equation down to the last X, (and the X will change) and the f will still be 1/X/X.

An almost one about 1,000 engineers in the world have learned this is an Easy and True

This is Harrell Geron, and engineer for almost 40 years.

Ragknot

• Changed type George.Zhao CHNMicrosoft contingent staff, Moderator 4 hours 30 minutes ago Experience Sharing

Hi Harrell Geron,

Thanks so much for sharing this. It's really valuable. Thanks again.

Regards,