Turbulent flow of a rough-wall pipe is simulated using Direct Numerical Simulations (DNS) at low and medium Reynolds number from the transitionally rough regime to the fully rough regime. The rough surfaces simulated consist of three-dimensional sinusoidal roughness elements. The size of the roughness (roughness semi-amplitude height h+ and wavelength λ+) is increased geometrically while maintaining the height-to-wavelength ratio of the sinusoidal roughness element. A method is developed to accurately calculate the roughness function ΔU+ for the simulations conducted at low Reynolds number. For this surface, the flow is fully rough when h+ ≈ 60 (simulated at Reτ = 540). This corresponds to k+s ≈ 4.1h+ where k+s is Nikuradse's equivalent sandgrain roughness. A linear trend is observed when the ratio of the apparent wall shear stress due to form drag on the roughness elements to the total wall shear stress Rτ = τR/τT is plotted against the log of the roughness height h+. This linear trend is also observed in the transitionally rough regime. For all the rough-wall pipe simulations conducted, Townsend's  outer layer similarity hypothesis holds true.