A simple model to extend 1-D hydraulics to 3-D hydraulics

the core of fluid mechanics is the study of friction on a solid/liquid interface, the friction force can be divided into skin friction and form drag. Nikuradse's experiments reveal that the friction factor depends on the Reynolds number (Re) and relative roughness (r), this observation implies the co-existence of skin friction and form drag, but the definitions of Re and r given by Nikuradse cannot be linked with the skin friction and form drag, this leads to the invalidity of existing theory to predict the friction factor in a complex flow, like a channel flow with vegetation. To establish a universal relationship, the hydraulic radius, Reynolds numbers and relative roughness are redefined, and the connection of these parameters with the skin friction and form drag is established. For the flowing fluid, the separation region is generated after passing the fluid, and these eddies form a "dead zone", this study reveals that the drag force is proportional to the volume of dead zone. By analyzing the measured data available in the literature, an equation has been established to express the drag force and the volume of dead zone, thus it provides an alternative way to interpret Nikuradse's work and extends the existing outcomes to complex flows. KEY WORDS: Hydraulic