Methanol is to be used as an entrainer in an azeotropic fractionator. Liquid ethanol is pumped from a storage tank on ground floor to a reactor on level $2$ at height Z$2$ using a centrifugal pump. The lowest liquid level in the tank is not allowed to go below the height of Z$1.$ Line segment L$1$ from the tank to the pump is a $3(1)/(2)$ inch schedule $40$ commercial steel, and is $20$ m long from the tank outlet to the pump inlet. This line segment has $3\backslash$times $90\backslash$deg standard long elbows and $1\backslash$times globe valve that is fully open. Line segment L$2$ from the pump outlet to the fractionator inlet is also a $3(1)/(2)$ inch schedule $40$ commercial steel, and is $90$ m long. The Segment L$1$ has $5\backslash$times $90\backslash$deg standard long elbows and $2\backslash$times globe valve that is fully open, $4\backslash$times gate valves $(2\backslash$times fully open, $2\backslash$times $(1)/(2)$ open$).$ The tank and fractionator are both at atmospheric pressure. The flowrate of methanol is $24$ tonnes$/$hr$.$ Estimate the power required by the pump by performing the following steps:

a$)$ Calculate the design static head of the system $($head in m$)[1]$

b$)$ Specify the piping dimensions of the system $($ID and OD in mm$)[3]$

c$)$ Provide the design flow specifications for the pump i$.$e$.$ flowrate $($m$3/$hr$)$ and velocity $($m$/$s$)[4]$

d$)$ Calculate the dynamic head of the system $($head in m$)[8]$

e$)$ Calculate the power required by the pump motor $[4]$

f$)$ If NPSH required by the pump is $6$m$,$ will the pump be able to do the required task? $[5]$

Z$1=1$ m$,$ Z$2=5$ m$,$ T $=30\backslash$deg C$.$ Take the pump efficiency as $70\%.$