# Numerical Study of Viscous Flow in the Hydraulic System of Electro Optical Tracking System

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## Abstract

In this chapter, we present a study of numerical simulation of centerline velocity, velocity contour and wall shear stress for a two dimensional viscous and incompressible fluid flow in rectangular pipe. The numerical results have been corroborated through a scaling law and asymptotic analysis. It deals with simulation of viscous flow in a typical hydraulic control system can be used in Electro Optical Tracking System (EOTS). Due to geometric constraint, the typical piping can be used in hydraulic circuit of EOTS is of rectangular (with aspect ratio *p* factor = 1) cross section. The two dimensional governing equation of laminar flow of highly viscous fluid is solved in the present work by using finite difference method. Through extensive simulation, the grid independence of centerline velocity and wall shear stress has been established in the present study. In addition a scale analysis approach and asymptotic analysis of the problem have been carried out. The axial velocity profile in 3D space and corresponding contour has been computed here. It has been demonstrated that the velocity contour is parabolic in nature. The present work also establishes the fact that the velocity profile remains parabolic for rectangular pipe with varying cross sectional aspect ratio (*p factor*). At different *p factor*, the centerline velocity and wall shear stress have also been presented in this chapter.

## Keywords

Viscous flow*p*Factor TDMA EOT

## Notes

### Acknowledgments

The authors are grateful to the Director, ITR for his permission towards the publication of this work.

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