The roughness effect is significant in the turbulent flow over a rough surface. The roughness increases the drag force and blockage effects, leading to increased pressure drop. The turbulent flow over the rough surface can be numerically modelled using wall-modelled Reynolds-averaged Navier-Stokes equations (RANS). The RANS approach uses the equivalent sand-grain roughness height (k_s) with wall functions to overcome the necessity of a very fine mesh to resolve each roughness element. Different formulas are available in the literature to find k_s based on the surface roughness statistics. In this work, a new wall function for turbulent viscosity is developed to incorporate the effect of roughness and validate it with the experimental data available in the literature. Further, the efficacy of the reported formulas for k_s is numerically verified with the experimental data for skin friction coefficient (C_ƒ) in turbulent flow through a rough channel. The simulation is carried out for the rough surfaces for different inlet Reynolds numbers (Re). It is observed that the proposed rough wall function can provide a nearly equal value of C_ƒ as the experimental data with a maximum error below 1%. Not all the published formulas of k_s show good agreement with the experimental data. Further, it is found that the dimensionless cell centre distance (y⁺) depends on Re and k_s.