$($c$)$ A venturi$-$meter shown below is being used to measure the flow rate of oil of relative

density of $0\mathrm{.}88$ flowing in $200$ mm diameter pipe. The pipe diameter of the venturi meter

is $200$ mm and the throat diameter is $100$mm$.$ The pressure difference between the

tapping points measured using a U$-$tube manometer is $18$k$($N$)/($m$^(2)).$ The velocity at the inlet

of the venturi meter has been measured to be $1\mathrm{.}55($m$)/($s$)$ and the discharge is $0\mathrm{.}049($m$^(3))/($s$).$ A

mercury manometer is attached to the taping points. The relative density of mercury is

$13\mathrm{.}6$ and C$\_($d$)$ is $0\mathrm{.}98.$

$($i$)$ Calculate the pressure difference in the tapping points as a head of oil.

Use any one of below two formulas to answer this question.

Q$=$C$\_($d$)$A$\_(1)[(2$gH$)/((($A$\_(1))/($A$\_(2)))^(2)-1)]^((1)/(2))$

Q$=$C$\_($d$)$A$\_(2)[(2$gH$)/(((1-($A$\_(2))/($A$\_(1))))^(2))]^((1)/(2))$

ii$)$ Calculate the difference in mercury levels in the manometer