## Problems

1. Plot the variation of the density specific impulse (product of average specific gravity and specific impulse) with mixture ratio and explain the meaning of the curve. Use the theoretical shifting specific impulse values of Figure 5-1 and the specific gravities from Figure 7-1 or Table 7-1 for the liquid oxygen-RP-1 propellant combination. Answers: Check point at r - 2.0; Is = 290; Id = 303; 5av = 1.01.

2. Prepare a table comparing the relative merits of liquid oxygen and nitric acid as rocket oxidizers.

### 3. Derive Eq. 7-1 for the average specific gravity.

4. A rocket engine uses liquid oxygen and RP-1 as propellants at a design mass mixture ratio of 2.40. The pumps used in the feed system are basically constant-volume flow devices. The RP-1 hydrocarbon fuel has a nominal temperature of 298 K and it can vary at about ±25°C. The liquid oxygen is nominally at its boiling point (90 K), but, after the tank is pressurized, this temperature can increase by 30 K. What are the extreme mixture ratios under unfavorable temperature conditions? If this engine has a nominal mass flow rate of 100 kg/sec and a duration of 100 sec, what is the maximum residual propellant mass when the other propellant is fully consumed? Use the curve slopes of Fig. 7-1 to estimate changes in density. Assume that the specific impulse is constant for the relatively small changes in mixture ratio, that vapor pressure changes have no influence on the pump flow, and that the engine has no automatic control for mixture ratio.

5. The vehicle stage propelled by the rocket engine in Problem 4 has a design mass ratio ff!//m() of 0.50 (see Eq. 4-6). How much will the worst combined changes in propel-lant temperatures effect the mass ratio and the ideal gravity-free vacuum velocity?

6. (a) What should be the approximate percent ullage volume for nitrogen tetroxide tank when the vehicle is exposed to ambient temperatures between about 50°F and about 150°F?

(b) What is maximum tank presure at 150°F.

(c) What factors should be considered in part (b)?

Answers: (a) 15 to 17%; the variation is due to the nonuniform temperature distribution in the tank; (b) 6 to 7 atm; (c) vapor pressure, nitrogen monoxide content in the oxidizer, chemical reactions with wall materials, or impurities that result in largely insoluble gas products.

7. An insulated, long vertical, vented liquid oxygen tank has been sitting on the sea level launch stand for a period of time. The surface of the liquid is at atmospheric pressure and is 10.2 m above the closed outlet at the bottom of the tank. If there is no circulation, what will be the temperature, pressure and density of the oxygen at the tank outlet? 