Question $6)$ You are tasked with designing a pipeline system for the transport of compressed carbon dioxide to sequestration sites as part of a carbon capture and storage $($CCS$)$ project. The system requires $C{O}_2$ to flow through $100$ km of commercial steel pipe with an internal diameter of $0\mathrm{.}39$ m at a mass flow rate of $5$ million tonnes per year. The $C{O}_2$ is compressed and cooled to its liquid state for ease of transport, and has a density of $850k\frac{g}{m^3}$ and dynamic viscosity of $53{10}^{-6}$Pas. You can neglect the pressure drop due to minor losses. $($Data for this problem taken from: Sean T$.$ McCoy, Edward S$.$ Rubin, An engineeringeconomic model of pipeline transport of $C{O}_2$ with application to carbon capture and storage. International Journal of Greenhouse Gas Control $2(2008)219-229.)$

$($a$)$ Calculate the pressure drop along the length of the pipe.

$($b$)$ Determine the required pressure head $($in terms of height$)$ that the pump must overcome to maintain the flow.

$($c$)$ Calculate the pumping power requirements to transport the $C{O}_2.$ Is this reasonable for a singular pump? Are there other options?