Problem $3$

The two$-$reservoir system shown in Figure $3$ consists of three concrete pipes with roughness $k_s=0\mathrm{.}35mm$ for all pipes and an elevation difference of $H=50m$ between two reservoir level. For minor losses consider: Kent $=0\mathrm{.}5($entry loss factor$),$ Kext $=0\mathrm{.}15($exit loss factor$).$ Ignore minor losses at diameter changes and consider the kinematic viscosity as: $v=1{10}^{-6}\frac{m^2}{s}$ and $g=9\mathrm{.}81\frac{m}{s^2}.$

a$)$ Calculate the flow rate between the two reservoirs.

$[8$ marks$]$

b$)$ A new alternative solution is being considered to link the two reservoirs consisting of one pipe having a constant diameter. The flow rate calculated in part $($a$)$ must be achieved and you can use the friction factor of Pipe $1$ in part $($a$)$ for the new pipe. A control valve will also be added to the system with a minor loss coefficient of $K_L$

$u=3\mathrm{.}2.$ What is the diameter required for the pipe?

$[6$ marks$]$

Problem $4$

Water flows in the system shown in Figure $4.$ The pressure at $A$ is measured as $p_A=543$kPa$(k\frac{N}{m^2}).$ If the head loss between A and $B$ is $h_{f(A-B)}=3\mathrm{.}5m.$

a$)$ Calculate the total flow rate in pipe $3$ joining $B-C$

$[3$ marks$]$

b$)$ Calculate the pressure at $C.$

$[3$ marks$]$

You may assume the friction factor, $=0\mathrm{.}018$ for all pipes, and the water density $r=1000k\frac{g}{m^3}.$ Ignore local losses at the pipe bends and junctions.

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