16.26 quiz #2	4/16/97
	Due 4/25/97

1. Consider a nozzle liner for a liquid fueled rocket. We need a preliminary assessment of a proposed design. The design is far from fixed, so you will have to look at the problem parametrically.
   
   The nozzle liner is 1 mm thick Inconel alloy, supported every 1 cm in the x direction, and "long" in the y direction. The boundary conditions on the x ends are not yet designed; look at both clamped or simple supported cases. In the y direction, you can assume Ny = 0 and ky = 0 (like the large deflection conditions you looked at before, although for different reasons).
   
   The outer surface is exposed to rocket flame, T = 2500 °C, hc = 1000-3000 w/m2K (exact value unknown!); the inner surface is exposed to liquid fuel, T = -240 °C, hc = 3000-10000 w/m2K.
   
   Three operating modes are of interest: start up (assume we start with the fuel flowing already, so the initial temperature is very cold); continuous operation (steady state); and failure of the flow of fuel (locally), which can be modeled by the back face suddenly becoming insulated instead of cooled.
   
   The things we need to know are
   
   
   1. What are the maximum stresses? Will yield occur under operating conditions? Which conditions are the worst? What design choices will decrease stress levels?
      
      
   2. What are the deflections, in particular the out-of-plane (z) deflections? Which conditions are the worst? What design choices will decrease them?
      
      
   3. Is operation without fuel flow for cooling possible? For how long??

   
   
   
   
   

2. It is proposed that the sagging observed in medieval cathedral window glass is due to creep under their own weight over the 800 years or so that they have been there. For 10cm high glass panes, sitting vertically and supporting only their own weight, what would the relaxation modulus have to look like for ~20% creep to take place in 800 years? Assuming that the material is "well behaved"­that the relaxation modulus goes down linearly with log(time) and the temperature dependence is exponential­propose a simple set of tests to confirm/deny the creeping window theory in finite time.