This paper reviews analytical solutions for the accelerated flow of an incompressible Newtonian fluid in a pipeline. This problem can be solved in one of two ways according to the (1) imposed pressure gradient or (2) flow rate. Laminar accelerated flow solutions presented in a number of publications concern cases where the two driving mechanisms are described by simple mathematical functions: (a) impulsive change; (b) constant change; (c) ramp change, etc. The adoption of a more complex and realistic description of the pressure gradient or flow rate will be associated with a profound mathematical complexity of the final solution. This is particularly visible with the help of the universal formula derived by several researchers over the years and discussed in this paper. In addition to the solutions strictly defined for laminar flow, an interesting extension of this theory is the theory of underlying laminar flow for the analysis of turbulent accelerated pipe flows (TULF model developed by García García and Alvariño). The TULF model extends the Pai model developed more than 60 years ago, which has been previously used for steady flows only. The discussed solutions extend the theory of analytical solutions of simplified two-dimensional Navier–Stokes equations and can be used not only to study the behavior of liquids during accelerating pipe flow but they can also be used to test the accuracy of commercial CFD codes.

The article presents the theoretical research on hydraulic processes occurring in hydraulic drives of transport machines. The research analysed the influence of hydrodynamic processes on the fluid flow characteristics following installation of angular fitting connections in pipeline systems. The analysis was based on the numerical simulations by Reynolds-averaged Navier–Stokes equations in 3D. The fluid flow in the hydraulic system pipeline connections were investigated for fluid flow rate up to 100 l/min. For numerical simulation, a mesh independence study was performed. By modeling. we obtained results of pressure drops, turbulence models, flow coefficients and energy losses at 45° and 90° angular fitting connections. The article compares the results obtained using the calculation method based on the standard of equivalent length fitting with the findings presented. The research conducted indicated that using the equivalent length method is not appropriate for studying angular fitting connections. It was found that additional investigations are necessary for each type of angular fitting connection.

Theoretical research on hydraulic processes occurring in aircraft hydraulic drives is presented in the studies. Installation of angular fitting connections in aircraft pipeline systems influences hydrodynamic processes and fluid flow characteristics analysed in the research. The provided analysis is based on a validated numerical model utilizing Navier–Stokes equations and the k-epsilon turbulence model. Fluid flow inside the aircraft hydraulic drive pipeline system was investigated with flow rates up to 100 l/min. A mesh independence study was conducted for numerical simulation of the fluid flow. The obtained results include fluid pressure drops, energy losses, and operational delays associated with fluid flow vortex formations at 45° and 90° angular fitting connections. Additionally, compared results from standard methods of calculation for angular fitting connections, including the equivalent length and equivalent length same shape methods.