Flow Stability and Friction Factor in Rough Channels

Abstract

It is well known that in steep channels, the flow becomes unstable when the Froude number exceeds some critical value. Instead of obtaining uniform flow, a short distance from the channel inlet, waves of various lengths, amplitudes, and phase velocities appear. These waves, traveling downstream and occasionally overtaking each other, are called roll waves. The value of the friction factor in open channels in unstable flow conditions is affected by the Froude number. Some formulas for the calculation of the friction factor in unstable flow conditions have been suggested by other authors. After these formulas are checked for smooth channels, the formulas for rough channels are compared with measurements. The critical Froude number, which is presented as a function of the Reynolds number, the channel roughness, the vertical velocity distribution coefficient, and the channel width, is an important parameter. A generalized formula is given to compute the friction factor both in smooth and rough channels in unstable supercritical flow conditions. The experiments carried out confirm the increase of the friction factor in unstable flow in rough channels.