Numerical modeling of DarcyWeisbach friction factor and branching pipes problem
First, a numerical algorithm for the friction factor in the DarcyWeisbach pipe friction head loss formula is developed by an effective linear iteration scheme of the ColebrookWhite equation, which precisely determines, with a small load of computations, the friction factor within the ranges of: 0<relative roughness<0.1 and 2103<Reynolds number<109. The developed subroutine can be adapted to any pipe friction loss parts of any pipe network problems. Next, the branching pipes problem is formulated as a system of non-linear equations, and an efficient, practical, and always convergent numerical algortihm for its solution is developed, in which the DarcyWeisbach equation is used for the friction losses, the friction factor being computed by the above-mentioned algorithm. The model can handle many reservoirs which are interconnected by pipes branching from a common junction in just a couple of seconds of execution time.
darcyweisbach friction factor branching pipes problem