Open channel flow friction factor: Logarithmic law

Abstract

The friction factor in open channel flow is considered to increase proportionally with wall roughness compared to that of pipe flow because of undulation at the free surface. The undulation is considered to be driven from the bottom and side walls. The increment factor associated with free surface undulation, shape distortion, and meandering is related to the Manning coefficient, and the incremented friction factor is substituted into the friction factor of circular pipe smooth (stretching) turbulent flow so as to yield the friction factor for open channel flow. The new equation for friction factor or mean velocity provides similar results to the Manning equation and the Ganguillet-Kutter (GK) equation for small streams. However, it is found that the Manning equation results in larger values of mean velocity in wide rivers compared with the GK equation and the new logarithmic equation based on the concept termed as "smooth turbulent," which appears inappropriate in describing the turbulent flow mechanism. Smooth turbulent may have to be denoted as "stretching turbulent" because of stretching of the velocity profile as the Reynolds number increases. Based on the comparison results with the other two empirical equations, the new logarithmic equation could be suitably adopted in open channel flows.