In the paper, being the first part out of two (the second one is focused on processes of heat transfer), results of the computer simulations of the flow in a circular pipe with a ball inserts turbulising the flow are presented. An influence of the diameter of balls and their longitudinal distance on a pressure drop in the turbulent flow as a function of the Reynolds number (for Re = 10,000 / 300,000) was analyzed. The investigations were carried out for different diameters of the balls (Db = 7,10,13,16 and 19 mm) and different distances between them (L = 20, 24, 28, 32, 36, 40, 48, 60 and 85 mm) at a constant inner diameter of the tube (Dp = 26 mm). The results indicate that for the whole tested range of ball diameters and their longitudinal arrangements, there is an analytical dependency which allows for expressing a friction factor by the relationship: f = A.Re-B. The constants A and B were functions of two variables: a dimensionless diameter of the ball (X = Db/Dp) and a dimensionless longitudinal distance between balls (Y = L/Dp). These two constants are closely related. They can be calculated analytically for the entire range of X and Y using a formula of the fourth order surface polynomial (15 coefficients of that polynomial are presented in the paper). The paper presents also experimental investigations carried out using a PIV (Particle Image Velocimetry) apparatus. A comparative analysis of selected inserts and numerical calculations was the goal. The obtained results show a good correlation between the experiment and computer modelling. (C) 2014 Elsevier Ltd. All rights reserved.