Question $4$: $[15$ marks$]$

Water flows through a $25$ cm $($length$)$ rotameter $($Type A$)$ with an internal diameter of $25$ mm at the top and $20$ mm at the bottom. The float has a diameter of $20$ mm $,$ a volume of $6\mathrm{.}933c{m}^3$ and a specific gravity of $6\mathrm{.}0.$

$A_{\text{t}\text{h}\text{e}\text{y}}^{\text{u}\text{a}\text{r}\text{r}}$

a$)$ Assuming that $\frac{A_2}{A_1}$ is negligible, what is the area $($in $m{m}^2$ to $3$ significant figures$)$ of the annulus when there is a flow of $400\frac{l}{h}r$ water? Assume $C_D=0\mathrm{.}96$

$[3]$

b$)$ Recalculate the area of the annulus assuming $\frac{A_2}{A_1}$ is not negligible $($in $m{m}^2$ to $3$ significant figures$).$ Assume a constant $C_D$ of $0\mathrm{.}96.$ Show at least three iterations in solving.

Also give the final value of the linear flowrate and Reynolds number.

c$)$ How far from the bottom is the float under these conditions $($in cm to $3$ significant figures$)?$

$[3]$

d$)$ How does a rotameter differ from an orifice plate? List at least $2$ differences.

e$)$ How would you have solved part $($b$)$ if $C_D$ was NOT assumed constant.

List the steps involved to complete the question. DO NOT recalculate.

Given:

Please help and give the answers in metres