Effect of Shape on Uniform Flow through Smooth Rectangular Open Channels

Available experimental data on friction in smooth rectangular channels were analyzed by a researcher and arrived at the relationship $1/\mathit{f}\prime$= 2 log $R\mathit{f}\prime$− 0.8, where R= 4VR/v and f′=f$\dot{s}$Ψ_p(P/R) for channels and f′=f for smooth pipes. Ψ_p(P/R) is a shape parameter. Values of P/R when b/y< 2 were indicated by an asterisk, and a relationship was obtained between P/R and Ψ_p(P/R). Two researchers analyzed the same data that were used by another researcher and concluded that two functions Ψ₁(P/b) =$\mathit{P}/\mathit{b}$ and Ψ₂(b/y) are required to reflect the shape parameter. However, they combined and obtained Ψ_K=Ψ₁/Ψ₂=f/f′. Ψ₂(b/y) was calculated and plotted against b/y. They noted that Ψ_K≡ 1/Ψ_p, but maintained that there is no good relationship between Ψ_p and P/R. In the present study, it is shown that based on the curve, the equation connecting Ψ_p(P/R) and P/R could be obtained, which fits the curve within 1% error. A plot P/R versus Ψ_p(P/R) is given for ready use.