Gas Dynamics Lecture Notes: Normal Shock

In elementary fluid mechanics utilizing ideal gases, a shock wave is treated as a discontinuity where entropy increases over a nearly infinitesimal region. Since no fluid flow is discontinuous, a control volume is established around the shock wave, with the control surfaces that bound this volume parallel to the shock wave (with one surface on the pre-shock side of the fluid medium and one on the post-shock side). The two surfaces are separated by a very small depth such that the shock itself is entirely contained between them. At such control surfaces, momentum, mass flux and energy are constant; within combustion, detonations can be modelled as heat introduction across a shock wave. It is assumed the system is adiabatic (no heat exits or enters the system) and no work is being done. The Rankine–Hugoniot conditions arise from these considerations.

Taking into account the established assumptions, in a system where the downstream properties are becoming subsonic: the upstream and downstream flow properties of the fluid are considered isentropic. Since the total amount of energy within the system is constant, the stagnation enthalpy remains constant over both regions. Though, entropy is increasing; this must be accounted for by a drop in stagnation pressure of the downstream fluid.

Gas Dynamics: Introduction to Shocks: Normal, Oblique shocks and Expansion Wave

 Shock is an abrupt discontinuity in the flow field. It occurs in flows when the local flow speed exceeds the local sound speed. More specifically, it is a flow whose Mach number exceeds 1.

Gas Dynamics - Flow through Nozzle derivation

The flow through a nozzle can be considered as a isotropic process. The isotropic process is the adiabatic reversible process.
No heat exchange between the system and surroundings.
No loss(frictional) within the system or with surroundings.

Gas Dynamics: C-D nozzle de Laval Nozzle

A de Laval nozzle (or convergent-divergent nozzle, CD nozzle or con-di nozzle) is a tube that is pinched in the middle, making a carefully balanced, asymmetric hourglass shape. It is used to accelerate a hot, pressurized gas passing through it to a higher speed in the axial (thrust) direction, by converting the heat energy of the flow into kinetic energy. Because of this, the nozzle is widely used in some types of steam turbines and rocket engine nozzles. It also sees use in supersonic jet engines.

Gas Dynamics: Area Vs Velocity Relationship Nozzle

To analyze the effect of change in stream tube cross sectional area on the characteristics of flow we consider:
1. Euler's equation for steady state one dimensional flow
2. Continuity Equation

Gas Dynamics Velocity of Sound

   Sound Speed represents the speed at which the medium transmits pressure disturbance. It also can be mentioned that the speed at which the particles transmit it's disturbance to the neighboring particle.

Gas Dynamics Continuity Equation Derivation

A continuity equation in physics is an equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations.

Continuity equations are a stronger, local form of conservation laws. For example, the law of conservation of energy states that energy can neither be created nor destroyed—i.e., the total amount of energy is fixed. But this statement does not immediately rule out the possibility that energy could disappear from a field in Canada while simultaneously appearing in a room in Indonesia. A stronger statement is that energy is locally conserved: Energy can neither be created nor destroyed, nor can it "teleport" from one place to another—it can only move by a continuous flow. A continuity equation is the mathematical way to express this kind of statement.