## Info

The Mach number M is, using Eq. 3-11,

Figure 3-3 shows the variations of the velocity, specific volume, area, and Mach number with pressure in this nozzle. At optimum expansion the ideal exhaust velocity v2 is equal to the effective exhaust velocity c and, from Eq. 3-16, it is calculated to be 1827 m/sec. Therefore, the thrust F and the specific impulse can be determined from Eqs. 2-6 and

A number of interesting deductions can be made from this example. Very high gas velocities (over 1 km/sec) can be obtained in rocket nozzles. The temperature drop of the combustion gases flowing through a rocket nozzle is appreciable. In the example given the temperature changed 1117°C in a relatively short distance. This should not be surprising, for the increase in the kinetic energy of the gases is derived from a decrease of the enthalpy, which in turn is proportional to the decrease in temperature. Because the exhaust gases are still very hot (1105 K) when leaving the nozzle, they contain considerable thermal energy not available for conversion into kinetic energy of the jet.

### Nozzle Flow and Throat Condition

The required nozzle area decreases to a minimum (at 1.130 MPa or 164 psi pressure in the previous example) and then increases again. Nozzles of this type (often called De Laval nozzles after their inventor) consist of a convergent section followed by a divergent section. From the continuity equation, the

F = mv2 = 1 x 1827 = 1827 N Is = c/g0 = 1827/9.80 = 186 sec

Pressure, megapascal 