QUESTION $3$

Water flows steadily from the large open Tank $(1)$ and through a $0\mathrm{.}09$ m diameter pipe to the outlet at Section $(2)$ with an outlet velocity of $9\mathrm{.}08\frac{m}{s}$ as shown in Figure Q$3.$ A mercury manometer is used to measure the pressure difference across the pipe. Given the density of water and mercury are $1000k\frac{g}{m^3}$ and $13600k\frac{g}{m^3},$ respectively. Based on the Bernoulli equation for Sections $(2)$ and $(3),$ determine the height of the manometer, h$.$ State all the assumptions used in your calculation. $($CO$1,$ PO$1,$ C$3)$

Figure Q$3$: Mercury manometer attached to piping system

$(9$ marks$)$