This paper deals with the numerical solution of the run-up flow of a viscous incompressible fluid through a pipe whose cross-section is an equilateral triangle. The problem is solved numerically, using a five-point formula. From this, it is observed that Reynold number has a great influence on the run-up flows. If it is large, the fluid comes to rest after a long time. It is also observed that on the line y = 2h, the decrease in velocity is nose symmetrical in the region. The region y > 4h is the region of silence. Hence it is concluded that Reynold numbers play an important role in run-up flows.

The problem of run-up flow of viscous incompressible fluid between rigid boundaries is attracting the attention of researchers due to its importance in several branches of technology. Kazakia and Riviln (1981) and Rivlin (1982) have investigated the run-up flow of viscoelastic fluids between parallel plates and circular geometrics. Pattabhi and Appala Raju (1984) studied the run-up flow in a generalized porous medium.

The aim of the present investigation is to examine the run-up flow of a viscous incompressible fluid through a pipe whose cross-section is an equilateral triangle. Initially, the flow is due to a constant pressure gradient. When a steady state is reached, the pressure is suddenly withdrawn, resulting in run-up flow. The effect of Reynold number on the flow field is studied. Unlike closed form solutions in infinite series, this investigation brings out graphically the velocity distributions at different times for different Reynold numbers.

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