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Friction factors were determined for fully developed turbulent flow of mercury in smooth concentric annuli under conditions where either both walls were unwetted, or both were wetted, or the inner wall was wetted and the outer one unwetted. Three radius ratios (r2/r1) were used, i.e., 2.09, 2.78, and 4.00. Unwetted walls gave the lowest friction factors, which were practically independent of the r2/r1 ratio over the limited range tested. The factors were 10 ± 1 percent higher than the commonly accepted values for smooth pipes (at the same Reynolds number). The highest friction factors were obtained with the inner wall wetted and the outer wall unwetted, and the greater the r2/r1 ratio the greater was the effect. For example, at r2/r1 = 4.00, the friction factors were 9.9% greater than for the situation when both walls were unwetted. The wetting conditions affected the location of the radius of maximum velocity (rm); and it was found that the nearer rm approached r2, the higher was the friction factor.