The truncated nozzle shown in the figure is used to monitor the mass flow rate of methane. The area of the nozzle is 3 cm², and the area of the pipe is 12 cm². The upstream total pressure and total temperature are 150 kPa absolute and 30°C. The back pressure is 100 kPa. 

a. Calculate the mass flow rate of methane. 

b. Calculate the mass flow rate assuming the Bernoulli equation is valid, with the density being the density of the gas at the nozzle exit.