b$)$ A pumping system is required as described below. On the following page you will find head vs flow curves for a $13"$ Pentair$-$Aurora pump, two of which are available, if necessary, for this system. Note that the NPSH values which are given are in units of feet. Graph paper is also given if needed. Details of the flows, pipes, fittings and other information are as follows:

Flows: minimum demand $\backslash (0\mathrm{.}20\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )$ at $40$ m pressure; maximum demand $\backslash (0\mathrm{.}32\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )$ at $25$ m $.$

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Pipes: All have Hazen$-$Williams C $=100$

NPSH $=$ Net Positive Suction Head

Intake: length: $\}200\backslash$textrm$\{$m

Inlet elevation: $\}2\backslash$textrm$\{$m$\}\backslash$mathrm$\{$ below the centre$-$line of the pump

minor fittings: I entrance, $2$ bends, $1$ check valve, $1$ gate valve, $1$ contraction, $1$

manifold split $($if needed for two parallel pumps$)$

Outlet: length: $\}\backslash$quad$2\mathrm{.}5\backslash$textrm$\{$km

minor fittings: $1$ expansion, $1$ check valve, $1$ gate valve, $1$ manifold join

$"$k$"$ values for the minor head$-$losses for each fitting:

entrance: $0\mathrm{.}2$

bend: $0\mathrm{.}4$

check valve: $0\mathrm{.}8$

gate valve: $0\mathrm{.}3$

contraction: $0\mathrm{.}07$

expansion: $\}0\mathrm{.}0$

manifold join: $0\mathrm{.}25$

manifold split: $0\mathrm{.}01$

$```$

Other information:

Water temperature is $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$; vapour pressure is $\backslash (1\mathrm{.}2\backslash$mathrm$\{$kPa$\}(0\mathrm{.}12\backslash$mathrm$\{$~m$\})\backslash )$; atmospheric pressure $\backslash (101\backslash$mathrm$\{$kPa$\}(10\mathrm{.}2\backslash$mathrm$\{$~m$\})\backslash ).$

Determine whether the available pump$($s$)$ will be satisfactory under all conditions of flow. $(23$ marks$)$