$1\mathrm{.}3*{10}^{-11}$kPa $)$ is pumped out of a cylindrical reservoir tank at $20C.$ The tank has a diameter of $3$

m and the liquid has an initial depth of $2\mathrm{.}5$ m $.$ Operationally, the tank is fed with cocoa butter at a

rate of $0\mathrm{.}25\frac{m^3}{s}($while simultaneously being drained by the pump$)$ and the pump's suction end

is located $1\mathrm{.}5$ m above the initial liquid surface. The riveted steel pipe leading from the tank to

the pump has a $25$ cm inner diameter, total length of $9$ m $,$ and a roughness of $3\mathrm{.}2$ mm $.$ Form

losses due to the elbow and expansions$/$contractions are negligible. Hence, the head loss

attributed to viscous friction in this pipe alone is $4\mathrm{.}3$ m $.$ The net positive suction head required by

the specific pump used is $4$ m $.$ The diagram below depicts the initial condition of the system.

a$.$ Estimate the volumetric flowrate in $\frac{m^3}{s}$ in the suction line feeding the pump. Use the

Colebrook correlation for frictional loss. State and confirm$/$justify any assumptions you

make.

b$.$ Calculate the following values as they pertain to operation of the process until cavitation

occurs in the pump:

i$.$ Quantity of cocoa butter delivered by the pump $(m^3),18m^3$

ii$.$ Time of operation $($s$)50$ sec