iii) starting with the chocked mass flow rate equation for isothermal ideal gas flow discharging through a small puncture in a vessel given by Y+1 27-1 m = = C,AP My RT (2) 5 where A is the ncti area, y the ratio of specific heat capacities, M molecular weight, C, discharge coefficient, with subscript, f denoting fluid, show that, the variation of the upstream pressure, P(t) in the vessel as a function of time (t), is given by: Pf0 P(t) = fit=0 GERT e MV (3) where V is the volume of the gas and 7+1 y-1 G1 = C,A My 2 RT, (y +1 (4) iv) Using equations (2) & (3) above along with ideal gas flow rate equation for unchoked flow, assuming that these hold for the case of a rupture in a pipe, determine the corresponding variation of mass release rate with time in the first 11 s following pipe failure, presenting the results in both in tabular and graphical forms at 0.5 s intervals. You may assume that post pipe failure, immediate transition of the liquid ammonia occupying the entire volume of the pipe to the gas phase occurs at constant temperature, and that the feed flow into the pipe is terminated immediately after failure using an emergency shutdown valve. In performing your calculations, clearly state any equations used along with the definitions of symbols. v) Calculate the corresponding amount (kg) of ammonia released based on the conditions stated in part iv) above in the first 11 s following pipe rupture, once again clearly stating any equations used including definitions of symbols (no need to show derivations)