Why do rockets have a diverging nozzle at the exit

This means that the exit flow from the nozzle will be subsonic and that we will have to reduce the pressure further to obtain a better working condition for the given nozzle. As seen in case E, reducing the exit pressure further results in a strange behavior in the gas flow.

During this operation condition, the exit pressure of the nozzle is below the ambient pressure. This makes exit flow converge and causes a strange shock wave formation after exiting the nozzle. These shock waves are not normal in this case and are more complex than any that we have encountered so far. However, the flow beyond the exit nozzle becomes a mixture of supersonic and subsonic flow, called overextended flow.

During this operation, the nozzle is inefficient, but usually the rocket engines are designed in this mode. This interesting flow pattern can be seen in the following figure. First figure show this pattern extending backward. The second figure shows a test case of this flow pattern in the sea elevation, meaning during liftoff. Why we use inefficient nozzle design during the lift-off. The answer to this question is simple. The answer will be clear to you when we study the next case.

For case F, the exit pressure is reduced even further and the rocket nozzle works in its optimum efficiency. There is no shock wave formation in the flow and the gas flow gets out from the nozzle almost at the same diameter as the diameter of the exit nozzle. The reason we used an inefficient flow for case E rather than case F, which is optimal, becomes clearer now.

Since the rocket is ascending after the lift-off, the outside pressure begins to fall from case E pressure towards case F pressure. This takes the rocket nozzle towards its optimum design condition, as shown here. For case G, what happens if we further reduce the exit pressure of the nozzle? Since the gas coming from the exit nozzle is at a higher pressure than the surrounding gas, the gas coming from the nozzle will expand outward as soon as it leaves the nozzle.

This flow behavior is also inefficient, since some thrust force goes outward from the rocket instead of going in the opposite direction of the rocket flight. This situation happens when the rocket is working in its optimum efficiency keeps ascending to the thinner part of the atmosphere. This flow pattern is called under expanded flow and can be seen in the Apollo Six test flights, in this image.

I hope this explanation helps you to better understand the inner workings of the converging diverging rocket nozzle.

Thank you for taking the time to watch our video. Now in our day to day lives, it is a common phenomenon that decreasing the cross-section of the nozzle increases the speed of the fluid going through it. A common experience when watering garden plants, where we decrease the cross-section of pipe at exit using our thumb, in order to increase the exit velocity of water and make it move through larger distance. Question is: To what limit, can we increase the fluid velocity by decreasing the area?

The figure you see above, whereby fluid velocity is increased by decreasing the area known as convergent nozzles is valid only for subsonic fluids. Meaning if the fluid final velocity is less than the speed of sound in that medium, the converging nozzle will accelerate it — till it reaches the speed of sound or Mach number 1. Beyond that, if it is further converged, the fluid velocity will start decreasing because of a phenomenon called Choking.

Now space is too narrow for the motion to happen and choking occurs whereby each molecule is staring each other! So, after choking occurs, the fluid has approached Mach 1. Beyond that to further increase the speed, the nozzle needs to diverge.

Then diverge to increase the speed further. In this way, there will appear a section at which the cross-section is smallest — that is called throat, the point where choking occurs. Note: Mach Number is a dimensionless number representing the ratio of flow velocity to the local speed of sound in that medium. 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 is exactly the opposite of what happens subsonically.

Why the big difference? Because in supersonic compressible flows, both the density and the velocity are changing as we change the area in order to conserve mass. For subsonic incompressible flows, the density remains fairly constant, so the increase in area produces a decrease in velocity to conserve mass.

But in supersonic flows, there are two changes; the velocity and the density.