B$.7($a$)$ Water is flowing upwards through a vertical pipeline which tapers from $300mm$ to $200mm$ diameter as shown in Fig. B$\mathrm{.}7$a$.$ A mercury manometer is connected to the pipeline to measure the flow. The vertical distance between the two taped points, Point $1$ and Point $2,$ is $1m$ and the manometer reading is $100mm.$ By assuming the erergy losses in the flow is negligible, determine:

$($i$)$ the pressure difference between Point $1$ and Point $2$;

$(4$ marks$)$

$($ii$)$ the velocity of the flow at Point $1$; and

$(6$ marks$)$

$($iii$)$ the flow rate.

$(2$ marks$)$