Problem $4-$ After a long workout, Andres Del$-$Valium wants a tall glass of "fresh" lukewarm water. To get that water out of his sewer pond, he designs a pumping system. His pipe diameter is $2$ cm $,$ its straight length is $10$ m $,$ his friction factor $0\mathrm{.}002,$ and his volumetric flow is $0\mathrm{.}002\frac{m^3}{sec}.$ If his total pump head available is $50$ m $,$ how many swing check values can he install and continue to flow this much material? Both ends of his piping system are open to atmospheric pressure, and you can neglect both kinetic head and potential energy effects.