On the History, Science, and Technology Included in the Moody Diagram

Abstract

This paper is a historical review of the science, both experimental and theoretical, behind the iconic Moody diagram used to avoid tedious iterations choosing pumps and pipes. The large body of historical pipe flow measurements and the choice of dimensionless groups and the Buckingham-Π theorem are also discussed. The traditional use of the Moody diagram to solve common pipe flow problem is discussed. Alternatives to the Moody diagram from the literature and novel ones presented here are shown to produce a solution without iteration for any type of pipe loss problem.

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

“…In that case compromise between reduction of maximal and average relative error is obtained. Also, fitness function can be set to reduce simultaneously mean square error δMSE and maximal relative error δ, as in (4). As already noted for (3), ratio between weight coefficients k3 and k4, determines influence of mean square error δMSE and maximal relative error δ in optimization.…”

“…It describes a monotonic change in the friction factor (λ) during the turbulent flow in commercial pipes from smooth to fully rough. Moody's and Rouse's charts [3,4] represent the plots of the Colebrook equation over a very wide range of the Reynolds number (R from 2320 to 10 8 ) and relative roughness values (ε/D from 0 to 0.05). Beside of some of its shortcomings [54], today, Colebrook's equation is accepted as the informal standard of accuracy for calculation of hydraulic friction factor (λ).…”

“…The Colebrook equation (1) relates hydraulic flow friction (λ) through Reynolds number (R) and relative roughness (ε/D) of inner pipe surface but in implicit way; λ=f(λ, R, ε/D) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. On the other hand, to express flow friction (λ) in implicit way a number of approximations can be used .…”

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

“…It describes a monotonic change in the friction factor (λ) during the turbulent flow in commercial pipes from smooth to fully rough. Moody's and Rouse's charts [3,4] represent the plots of the Colebrook equation over a very wide range of the Reynolds number (R from 2320 to 10 8 ) and relative roughness values (ε/D from 0 to 0.05). Besides some of its shortcomings [54], today, Colebrook's equation is accepted as the informal standard of accuracy for the calculation of the hydraulic friction factor (λ).…”

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

“…The Colebrook Equation (1) relates hydraulic flow friction (λ) through the Reynolds number (R) and the relative roughness (ε/D) of the inner pipe surface, but in an implicit way; λ = f(λ, R, ε/D) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. On the other hand, to express flow friction (λ) in an explicit way, a number of approximations can be used; λ ≈ f(R, ε/D) .…”