How is the exit velocity of the flow in a sounding rocket nozzle?

Question

How is the exit velocity of the flow in a sounding rocket nozzle? Is it subsonic or supersonic?

Is a de Laval nozzle required for sounding rockets?

Bonus Question: What about Model Rockets?

Answer 1

Essentially all practical rocket engines have supersonic exhaust velocities. This includes model rockets!

The force (thrust) generated by a rocket engine is given by $$F=\dot{m}V_e$$

where $F$ is the thrust, $\dot{m}$ is the rate of propellant mass flow from the nozzle (in units like kg/s), and $V_e$ is the exhaust velocity. Note that the force is directly proportional to the exhaust velocity. If you want to produce a certain level of thrust, doing it with $V_{e1}$ half as large as $V_{e2}$ means you have to feed twice as much propellant per second into engine 1 than for engine 2. Due to the exponential nature of the Tsiolkovsky rocket equation $$\Delta V=V_e \ln \frac{m_o}{m_f}$$ where $\Delta V$ is the velocity you need to impart to the rocket, $m_f$ is the mass of the rocket (and everything still attached to it) after the burn ends, and $m_o$ is the mass at the start of the burn ($m_o = m_f + m_p$, where $m_p$ is the mass of the propellant used), this means you have to carry more than twice as much propellant to get the same $\Delta V$, assuming $m_f$ doesn't change.

Or, if both $m_f$ and $m_p$ are fixed, the $\Delta V$ you'd get from engine 1 is half as much as you'd get from engine 2.

The net result: high $V_e$ is always good, unless getting higher $V_e$ adds significantly to $m_f$, as is sometimes the case with electric propulsion engines like ion engines. It is possible to build a subsonic nozzle for a rocket engine, but building a supersonic nozzle doesn't take much more mass (or money), so you wind up ahead with the supersonic nozzle, even for cheap little engines like model rocket engines.

There are many examples of subsonic nozzles in the world—but they aren't rocket engine nozzles.