On this slide we derive the equations which explain and describe why a supersonic flow accelerates in the divergent section of the nozzle while a subsonic flow decelerates in a divergent duct. We begin with the conservation of mass equation :. If we differentiate this equation, we obtain:.
This is Equation 10 on the page which contains the derivation of the isentropic flow relations We can use algebra on this equation to obtain:. This equation tells us how the velocity V changes when the area A changes, and the results depend on the Mach number M of the flow. If the flow is subsonic then M 0. This effect is exactly the opposite of what happens subsonically. Why the big difference? Because, to conserve mass in a supersonic compressible flow, both the density and the velocity are changing as we change the area.
For subsonic incompressible flows, the density remains fairly constant , so the increase in area produces only a change in velocity. But in supersonic flows, there are two changes; the velocity and the density. The equation:. To conserve both mass and momentum in a supersonic flow, the velocity increases and the density decreases as the area is increased.
Activities: Guided Tours Navigation.. And therefore for our case i. It is a completely irreversible process takes place in the Convergent divergent type of nozzles or in venturi at the divergent section.
A sudden change in pressure, temperature, and flow velocity takes place while supersonic flow was taking place. After shock flow becomes subsonic and stays subsonic till end. Width of this shock is very less i. Few examples of the application of convergent divergent type of nozzles in engineering are:. C-D nozzles can be seen in water supply pumps or in formula car intake system or in jet engines for providing sufficient thrust to propel at high speeds mostly in supersonic jets.
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