A large, uncooled, uninsulated, low-carbon-steel thrust chamber burned out in the throat region during a test. The wall (0.375 in. thick) had melted and there were several holes. The test engineer said that he estimated the heat transfer to have been about 15 Btu/in.2. The chamber was repaired and you are responsible for the next test. Someone suggested that a series of water hoses be hooked up to spray plenty of water on the outside of the nozzle wall at the throat region during the next test to prolong the firing duration. The steel’s melting point is estimated to be 2550 ∘F. Because of the likely local variation in mixture ratio and possibly imperfect impingement, you anticipate some local gas regions that are oxidizer rich and could start the rapid oxidation of the steel. You therefore decide that 2150 ∘F should be the maximum allowable inner wall temperature. Besides knowing the steel weight density (0.284 lbf/in.3), you have the following data for steel for the temperature range from ambient to 2150 ∘F: the specific heat is 0.143 Btu/lbm-∘F and the thermal conductivity is 260 Btu/hr-ft2-∘F/in. Determine the approximate time for running the next test (without burnout) both with and without the water sprays. Justify any assumptions you make. If the water spray seems to be adequate (getting at least 10% more burning time), make sketches with notes on how the mechanic should arrange for this water flow during testing so it will be most effective.