In the metal additive manufacturing field, laser powder bed fusion process has been proposed in recent years to improve the efficiency of compact heat exchangers and microchannels cooling applications. The possibility to design high performing unconventional geometries opens novel frontiers in advanced cooling applications. Depending on the manufactured geometry and the process conditions, one of the main limiting factors of metal additive manufacturing can be the complex surface texture with high roughness, which for some applications can become a critical issue. For example, in cooling channels made via laser powder bed fusion, pressure drop can be difficult to predict due to the combined effects of surface texture and the final sizes of the cross-section of the channels. Both these factors depend upon the channel orientation during the manufacturing process. In this work, the water pressure drops of five different straight channels are investigated. The samples were made of CuCrZr copper alloy and built at different sloping angles with respect to the platform plane: 0° (horizontal), 45°, 60°, 75° and 90° (vertical). The sizes of each channel were measured by X-ray computed tomography. The five samples were experimentally tested by varying the Reynolds number from 2400 to 44700 in order to investigate the fluid flow in transitional and turbulent flow regimes. Then, each sample was cut into four longitudinal parts and each channel internal wall surface was characterized using an optical device and computing the areal surface texture parameters. As a result, a novel method is proposed to correlate the surface texture characteristics of each building orientation channel wall to the mean hydraulic absolute roughness, by taking Moody's diagram for rough pipes as a reference.