Question $1.$

$($a$)$ A $3$ m wide sluice gate on a tank of water that is a circular quadrant of radius $R=1\mathrm{.}5m$ is pivoted as shown. Calculate the magnitude and direction of the resultant force when the water level is

$($i$)$ as shown with $D=2\mathrm{.}5m$

$($ii$)0\mathrm{.}5$ m below the pivot

piv

$[8$ marks$]$

$($b$)$ A circular butter$-$fly valve of diameter $1\mathrm{.}4$ m is fitted to the vertical side wall of a tank containing water with the level of water above the centre of the valve being $\frac{?}{\text{b}\text{a}\text{r}}(z)=5m.$

What is the torque required at the pivot to open the valve?

CIVE$1460$: Problem Sheet $1$

Water Engineering

$($c$)$ Water flows in a circular pipe which increases in diameter from $300$ mm at point A to $350$ mm at point B$.$ Then pipe then splits into two branches of diameters $0\mathrm{.}25$ m and $0\mathrm{.}2$ m discharging at $C$ and $D$ respectively. If the velocity at $A$ is $1\mathrm{.}0\frac{m}{s}$ and at $D$ is $0\mathrm{.}8\frac{m}{s},$

$($i$)$ What are the discharges at $C$ and $D$ and the velocities at $B$ and $C?$

$($ii$)$ If point $A$ is $4$ m higher than point $B$ and the pressure at $A$ is $14k\frac{N}{m^2},$ what is the pressure at point $B?$

$[9$ Marks$]$

need to solve all parts

please do it urgently

please do not copy paste chegg previous solution

need to do it correctly.its my test

please do complete Q$1$ including all part a$,$b$,$c