# Rocket Propulsion and Bernoulli's Theorem

This is what my textbook says on rocket propulsion:
$\hspace{75px}$ Questions:

1. The beginning of the textbook excerpt says that the fuel is converted into a gas at high pressure. Does this mean that, according to Bernoulli's Theorem, the velocity of the gas will be low?

2. But doesn't the fact that there is a velocity thrust contradict the above statement?

3. Is the shape of the nozzle responsible for this?

I’ll just address the two parts together. Bernoulli’s equation is about how pressure and velocity change as a bit of fluid moves along a flow line. It comes from the conservation of the energy of that bit of fluid.

So let’s follow it along. In the combustion zone, the gas is hot and under high pressure, but not moving very fast. Next it goes through the nozzle, where the gas speeds up and the pressure drops. This initially reaches its limit when the pressure has dropped to atmospheric pressure right at the end of the nozzle. At that point the gas is moving as fast as it can, and as much of the combustion pressure as possible has been converted to velocity. (You want that to get maximum thrust)

In space, you can take that further, dropping the exhaust to even lower pressure and getting more speed. More speed is more thrust. This is an advantage of having a “vacuum” engine on a rockets upper stage.

Another way to think of it, not using Bernoulli’s equation but just as valid, is to think about the gas in the middle of the nozzle. It has high pressure pushing hard from the combustion chamber side, and much less pressure pushing from the atmosphere/vacuum side. What will it do? It’ll accelerate away from the combustion chamber toward the outside, gaining speed as it does.

• So, when the gas in the nozzle speeds up, low pressure will be created. But this low pressure in the nozzle- will it be greater than atmospheric pressure ? – Gokulakrishnan Shankar Mar 26 '18 at 10:50
• Is the area of the nozzle mentioned here the top part of the nozzle or the base? – Gokulakrishnan Shankar Mar 26 '18 at 10:54
• First, speed doesn’t create low pressure as such. It’s more like it happens the other way: a decrease in pressure causes a net force that accelerates, hence speeds up, the fluid. The gases start at high pressure and drop to lower, eventually reaching atmospheric pressure at the exit. – Bob Jacobsen Mar 26 '18 at 18:50

Bernelli's equation is only applicable to point where fluid travel sub sonic. To my knowledge the convergent section of nozzle/chamber uses bernelli's. As the the volume of the chamber is reduced the gas velocity increases. At the point it reaches supersonic speed it no longer necessarily apply. So the typical design stop here.

If we were to leave as so we would realize that a lot of energy is present still in the gas because when it leaves the rocket the plume expands a great deal in the radial direction. Now additional energy can be harnessed using the supersonic gas pressure to further accelerate the das in axial direction.

It is my guess that a reaction force is used from the walk of the nozzle. All's the nozzle has to do is expand at less rate than the gas does on its own. So a long tube after maximum convergence is all's that needed, that stops when gas pressure is near atmospheric pressure.