Natural gas, with k ≈ 1.3 and a molecular weight of 16, is to be pumped through 100 km of 81-cm-diameter pipeline. The downstream pressure is 150 kPa. If the gas enters at 60°C, the mass flow is 20 kg/s and f = 0.024, estimate the required entrance pressure for
(a) Isothermal flow and
(b) Adiabatic flow.