In this numerical study, we investigate fluid flow through rough microchannels using the Weierstrass-Mandelbrot function to model surface roughness. Key parameters such as velocity profiles, streamline patterns, and pressure drops are analyzed, focusing on the impact of different average roughness values. The Weierstrass-Mandelbrot function accurately represents fractal surfaces, providing a realistic examination of fluid dynamics. Our findings reveal that surface roughness significantly affects velocity distribution, with increased roughness causing more pronounced velocity gradients and potential turbulent-like behaviors at low Reynolds numbers. Streamline analysis shows that smoother channels exhibit uniform patterns, while rougher channels display complex and irregular flow paths, leading to increased mixing and enhanced heat and mass transfer in some microfluidic applications. Pressure drop analysis indicates that higher roughness leads to increased resistance to fluid flow, which is crucial for designing efficient microfluidic devices. Balancing roughness is essential for achieving desired fluidic resistance and performance. This study highlights the importance of precise control over surface roughness in microfluidic device fabrication. In conclusion, the study offers insights into the impact of roughness on velocity profiles, streamline patterns, and pressure drops, essential for optimizing microchannel designs in various applications.