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Natural gas is to be delivered across the country in a I ft pipeline at 50 kg/h. The delivery pressure needs to be at least 1 barg. Derive the correlation equation between the inlet pressure and the maximum pipe length. Consider isothermal flow at 25 C and 35 C, compare the minimum inlet pressure required to account for temperature fluctuations. Assume fF = 0.0030 and ideal gas behaviour. Justify any further assumptions made and validate your calculation