Problem $1$:

Consider the flow system sketched below. The fluid is water, and the pump is a centrifugal

pump.

Suppose the pump is operated in free$-$delivery

conditions. The pipe has an inlet and outlet diameter of

$2\mathrm{.}0$ cm and can has essentially zero roughness. The

minor loss coefficients for the loop are shown in the

below table. The contraction at the exit reduces the

diameter by $60\%$ of the pipe diameter. The minor loss

coefficient is based on the average exit velocity, not the

average pipe velocity. The total pipe length is $8\mathrm{.}75$ m $,$

and the elevation difference is $z_1-z_2=4\mathrm{.}6m.$

$($b$)$ Estimate the volume flow rate through this piping system under

these conditions. $($Ans: $34\mathrm{.}4$ litres $\frac{?}{\text{m}\text{i}\text{n}})$