$(35$ points$)$ An oil is to be pumped from a large open tank to a large pressurized tank held at

$250$kPa gauge. The oil $($specific gravity $=0\mathrm{.}85,$ density $=848k\frac{g}{m^3},$ viscosity $=2{10}^{-3}k\frac{g}{m}\frac{?}{s})$ is

to be pumped from an inlet at the side of the open tank through a line of commercial steel pipe

having an inside diameter of $0\mathrm{.}082m$ and total length of $150m.$ The desired nominal flow rate is

$12\frac{m^3}{h}$ and maximum flow rate is $15\frac{m^3}{h}.$ The complete piping contains four elbows $(90)$ and a

globe valve half open. In order to build a control system $($or mechatronics system$)$ for flow control

of this fluid pumping process, the plug type of the control valve must be determined and two

option is available: i$)$ inherently linear valve and ii$)$ inherently equal percentage valve $(a=40).$ As

a mechatronics engineer, find the installed characteristic curves of the both valves. Which one of

the valve is more suitable for this mechatronics$/$control system? Explain your reasoning. The

pump curve is given below. Hint: Valve pressure drop $=$ pump head $-($end pressure $+$ piping

$($pipe$,$ valve, elbows etc.$)$ pressure drop$)$ and we usually select $C_V$ value at maximum flow for our

valves.

You are free to use a spreadsheet software for calculating and$/$or plotting the installed

characteristics curves of the valves. You can prepare your graph by hand if you want

and a neat$/$readable graph is acceptable. However, you must show at least one data

point full calculation to get point$/$score from this question.