(a) Gaseous hydrogen at a constant pressure of 0.658 MPa

Chapter 6, Problem 6.D3

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(a) Gaseous hydrogen at a constant pressure of 0.658 MPa (5 atm) is to flow within the inside of a thin-walled cylindrical tube of nickel that has a radius of 0.125 m. The temperature of the tube is to be 350C and the pressure of hydrogen outside of the tube will be maintained at 0.0127 MPa (0.125 atm). Calculate the minimum wall thickness if the diffusion flux is to be no greater than 1.25 * 10-7 mol/m2 # s. The concentration of hydrogen in the nickel, CH (in moles hydrogen per cubic meter of Ni), is a function of hydrogen pressure, PH2 (in MPa), and absolute temperature T according to CH = 30.81pH2 exp a - 12,300 J>mol RT b (6.34) Furthermore, the diffusion coefficient for the diffusion of H in Ni depends on temperature as DH(m2>s) = 4.76 * 10-7 exp a - 39,560 J>mol RT b (6.35) (b) For thin-walled cylindrical tubes that are pressurized, the circumferential stress is a function of the pressure difference across the wall (p), cylinder radius (r), and tube thickness (x) according to Equation 6.25that is, s = r p x (6.25a) Compute the circumferential stress to which the walls of this pressurized cylinder are exposed. (Note: The symbol t is used for cylinder wall thickness in Equation 6.25 found in Design Example 6.2; in this version of Equation 6.25 (i.e., 6.25a) we denote wall thickness by x.) (c) The room-temperature yield strength of Ni is 100 MPa (15,000 psi), and sy diminishes about 5 MPa for every 50C rise in temperature. Would you expect the wall thickness computed in part (b) to be suitable for this Ni cylinder at 350C? Why or why not? (d) If this thickness is found to be suitable, computethe minimum thickness that could be usedwithout any deformation of the tube walls. Howmuch would the diffusion flux increase with thisreduction in thickness? However, if the thicknessdetermined in part (c) is found to be unsuitable,then specify a minimum thickness that you woulduse. In this case, how much of a decrease in diffusionflux would result?