Exact equations for pipe-flow problems

Discussers Ali R. Vatankhah and Salah Kouchakzadeh from Irrigation and Reclamation Engineering Department, University of Tehran, have presented their views on the work done by the authors of the Journal of Hydraulic Research on exact equations for pipe-flow problems. Discussers point out that although the maximum error related to equation (35) in their research for D over the complete range of relative roughness, ε/D, and R= Reynolds number encountered in practice is marginally higher than 2%, it is restricted to less than 0.6% for applications in practice. Discussers pinpoint that the error related to equation (20) by using five terms of the series is relatively high. Using five terms from that of equation (10) for the entire range of ε/D and R, the deviations of equation (20) in the authors' research indicate that the maximum error related to equation (20) reaches around 100%.