If the speed of the object is much less than the speed of sound of the gas, the density of the gas remains constant and the flow of gas can be described by conserving momentum and energy. As the speed of the object increases towards the speed of sound, we must consider compressibility effects on the gas. The density of the gas will vary locally as the gas is compressed by the object. For compressible flows with little or small flow turning, the change in flow properties are given by the isentropic relations because the flow process is reversible and the entropy is constant. But when an object moves faster than the speed of sound and there is an abrupt decrease in the flow area, shock waves are generated.
Shock waves are very small regions in a gas where the gas properties change by a large amount.
Across a shock wave, the air pressure increases almost instantaneously. The air temperature and density also increase across a shock wave, while the Mach number and speed of the flow decrease. The flow across a shock wave is irreversible , the entropy increases and the isentropic relations cannot be used. If the shock wave is perpendicular to the flow direction it is called a normal shock. On this slide we have listed the equations which describe the change in flow variables for flow across a normal shock.