A gas flows along a pipe of diameter D at a rate of m kg/s. Show that the pressure gradient is dp_32C, mRT pD dL Methane gas is passed through a pipe 500 mm diameter and 40 km long at 13 kg/s. The supply pressure is 11 bar. The flow is isothermal at 150C. Given that the molecular mass is 16 kg/kmol and the friction coefficient C is 0.005 determine a. the exit pressure. b. the inlet and exit velocities. c. the rate of heat transfer to the gas. d. the entropy change resulting from the heat transfer. e. the total entropy change calculated from the formula ds = Cp In(T2/T1) - R In(p2/p1)