  The study of fluids has been a topic of intense research for several hundred
years. Over the years, this has further increased due to improved computational
facility, which makes it easy to numerically simulate the fluid dynamics, which
was beyond the analytical reach before. In this project, we discuss the general
transport theorem for moving control volume system, apply this theory to
control mass system which gives the continuity equation, and on momentum
conservation from which we get the Navier-Stokes equation and energy
conservation. By approximating the three equations for the ideal gas flow, we
get one dimensional Euler equation. These equations are non-linear, and their
analytic solutions are highly non-trivial. We will use Riemann solvers to get
the exact solution numerically. In this project, we have considered only the
Sod's Shock Tube problem. Finally, we focus on the exact and approximate
solution of density, pressure, velocity, entropy, and Mach number using Python
code.
