$4\mathrm{.}29$ Two Bell & Gossett Series $80-$ SC $227$ pumps operating at $1750$ rpm are

connected in parallel. A third pump, a Bell & Gossett Series $80-$SC $227$

pump operating at $3500$ rpm is connected in series with the parallel pumps as

shown in Figure P$4\mathrm{.}29.$

FIGURE P$4\mathrm{.}29$

This composite pump combination is connected to a pipe network with the

following system curve:

$H_p=10[ft]+0\mathrm{.}0115[\frac{ft}{gp{m}^2}]A{A}^{}{?}^2$

Determine the following for this system:

a$.$ The system curve up to $140$ gpm

b$.$ The composite pump curve up to $160$ gpm

c$.$ The operating point $($head and capacity$)$ of the combined pump and pipe

system