Water surface roughness measurement and its potential effect on air–water interaction in a partially filled circular pipe

The water surface roughness and its potential effect on the air flow in the headspace of a circular pipe were investigated. A phase-detection intrusive conductivity probe was fabricated, achieving a sampling rate 50 times higher and a special resolution 84 times smaller than a regular ultrasonic sensor. Two dimensionless parameters were introduced to characterize the water surface roughness under varying hydraulic conditions in free surface flow within a circular pipe. It was found that the water surface roughness is primarily correlated with the Froude number of the water flow. Flow with a higher Froude number corresponds to a higher air–water transition thickness but a lower ratio between the actual and projection air–water contact area. This indicates that water surface fluctuations in higher Froude numbers have higher amplitudes but lower frequencies, and vice versa. A corrected drag coefficient considering the water surface roughness was proposed for describing the momentum transfer from water to air flow in a circular pipe. The corrected drag coefficient is mainly related to the Froude number of the water flow. The proposed drag coefficient effectively reflects a more fundamental mechanism of air–water interaction for free surface flow in a circular pipe.