3.4—Piping and Pumping Problems 135 Fig. 3.10 Fanning friction factor for flow in pipes. The turbulent region is based on the Colebrook and White equation. Pipe roughness. The question immediately arises as to how a roughness length scale ε can be assigned to the surface of a particular wall material. Initially, Nikuradse conducted pressure-drop measurements on pipes that he had artificially roughened by coating their inside walls with glue and sprinkling on a single layer of sand grains of known diameter.4 The situation is idealized in Fig. 3.11, where ε is the diameter of the sand grains. 4 J. Nikuradse, “Strōmungsgesetze in rauhen Rohren,” VDI-Forschungsarbeiten, No. 362 (1933).