Explicit design of commercial pipes with secondary losses

Design problems of single-lined pipe flow hydraulics are primarily concerned with determining pump power, pipe slope, discharge or pipe diameter or sometimes two of them. This study develops explicit approximate equations for the determination of pump power, discharge or pipe diameter, considering the gravity on a slope and pump power as two driving forces and skin friction and form drag as two balancing forces. A power law is introduced to represent the friction factor to account for the skin friction. When secondary losses are included in the governing equation, implicit equations are inevitably the result even if the power law of friction factor is used. By determining major non-dimensional physical numbers affecting the physical processes involved, approximate explicit equations are obtained from the computation results. Furthermore it is found that the ratios to account for the secondary losses are inversely or regularly proportional to the power of various non-dimensional physical numbers.