In this exercise, you are tasked with analyzing the pressure drop and energy loss in a natural gas flow system. The gas flows through a $1-$inch carbon steel pipeline consisting of several sections: a horizontal section $(2$ inch$),$ a vertical section $30$ inch which is connected via a $90\backslash$deg elbow fitting to another horizontal section $15$ inch, followed by a DN$20$ brass ball valve. After the valve, the gas flows through another $2-$inch horizontal section before reaching the outlet. The gas pressure at the inlet is $25$ PSIG and the outlet is $5$ PSIG. The flow is assumed to be turbulent. You are asked to calculate the pressure drop and energy loss due to the friction in the pipe and the effects of the valve and elbow fittings.

$1.$ Calculate the flow rate of the gas across the pipeline.

$2.$ Calculate the pressure drop across each section of the system, including the straight pipe segments, the elbow fitting, and the ball valve.

$3.$ Determine the total energy loss in the system due to frictional losses, given the flow conditions.

Additional Data:$-$ Gas viscosity: $0\mathrm{.}015$ cP$,$ Gas gravity: $0\mathrm{.}6,$ Gas compressibility factor: $0\mathrm{.}8,$ Gas compressibility: $6$e$-4$ psi e$-1,$ Gas inlet pressure: $25$ PSIG, Gas outlet pressure: $5$ PSIG, Temperature: $70\backslash$deg F$,$ Flow is turbulent.