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PjP,

FIGURE 3-^4. Area and velocity ratios as function of pressure ratio for the diverging section of a supersonic nozzle.

Example 3-3. Design a nozzle for an ideal rocket that has to operate at 25 km altitude and give 5000 N thrust at a chamber pressure of 2.068 MPa and a chamber temperature of 2800 K. Assuming that k = 1.30 and R = 355.4 J/kg-K, determine the throat area, exit area, throat velocity, and exit temperature.

SOLUTION. At 25 km the atmospheric pressure equals 0.002549 MPa (in Appendix 2 the ratio is 0.025158 which must be multiplied by the pressure at sea level or 0.1013 MPa). The pressure ratio is

Pi/P\ = Pi/Pi = 0.002549/2.068 = 0.001232 = 1/811.3

The critical pressure, from Eq. 3-20, is p, = 0.546 x 2.068 = 1.129 MPa

The throat velocity, from Eq. 3-23, is v, = —-RT\ =J2* L3,° 355.4 x 2800 = 1060 m/sec ' y k+ 1 1 V 1.3 + 1

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