The paper presents the results of a numerical study devoted to the hydraulic properties of a network of parallel triangular microchannels (hydraulic diameter Dh = 110 um). Previous experimental investigations had revealed that pressure drop through the microchannels system dramatically increases for the Reynolds number exceeding value of 10. The disagreement of the experimental findings with the estimations of flow resistance based on the assumption of fully developed flow were suspected to result from the so-called scale effect. Numerical simulations were performed by using the classical system of flow equations (continuity and Navier-Stokes equations) in order to explain the observed discrepancies. The calculations showed a very good agreement with the experimental results proving that there is no scale effect for the microchannels considered, i.e. the relevance of the constitutive flow model applied was confirmed. It was also clearly indicated that the excessive pressure losses in the high Reynolds number range are due to the secondary flows and separations appearing in several regions of the microchannel system.