For uniform flow in open channel, Bernoulli's equation for energy loss is where s is the head loss (in ft per unit length measured along the bottom slope of the channel), f is the friction factor, v...

For uniform flow in open channel, Bernoulli's equation for energy loss is

where s is the head loss (in ft per unit length measured along the bottom slope of the channel), f is the friction factor, v is the mean velocity, and R is the hydraulic radius (Area/wetted perimeter). The mean velocity, v, in an open channel depends on the hydraulic radius, R, the kinematic viscosity, v, the roughness height, k, and g, the acceleration of gravity. Show by dimensional analysis (apply the systematic analysis), Use v and R as the Q's.