QUESTION SET $2$: $(3$ QUESTIONS$)$ PLEASE ANSWER CAREFULLY WITH DETAILED SOLUTION. THANK YOU! $($see pictures$)$

$1.(3$ points$)$ A pump is a device that moves fluids from source to

destination by mechanical action.

a$.$ Classify two main types of pumps, based on their operating principles.

b$.$ As shown in Fig. $1,$ an oil pump is drawing $25kW$ of electric power while pumping oil with $=860k\frac{g}{m^3}$ at a rate of $0\mathrm{.}1\frac{m^3}{s}.$ The inlet and outlet diameters of the pipe are

$10cm$ and $12cm,$ respectively. If the pressure rise of oil in the pump is measured to be

$250$kPa and the motor efficiency is $90$ percent, determine the mechanical efficiency of

the pump. Take the kinetic energy correction factor to be $1\mathrm{.}05$ and the piping loss is

negligible.

$2.(4$ points$)$ A slurry comprising $40\%$ by mass solid is to be filtered

on a $2m$ diameter and $2m$ length rotating drum filter that ordinarily runs with $40\%$ of its

surface immersed in the slurry and under a pressure of $18k\frac{N}{m^2}.$ A laboratory test on a

sample of the slurry using a $200c{m}^2$ leaf filter coated with the same fabric as the drum

generated $300c{m}^3$ of filtrate in the first $60$ seconds and $140c{m}^3$ in the next $60$ seconds

when the leaf was subjected to an absolute pressure of $18k\frac{N}{m^2}.$ The dry cake had a bulk density of $1500k\frac{g}{m^3},$ whereas the filtrate had a density of $1000k\frac{g}{m^3}.$ The minimal cake thickness that could be easily detached off the fabric was $5mm.$ What speed should the drum revolve at for optimal throughput, and what is the total mass of slurry fed to the unit per unit time?

$3.(3$ points$)$Consider a centrifuge used for the separation of particles

from a liquid mixture in an industrial setting. The centrifuge has a rotor with a radius of $0\mathrm{.}15$ meters and is rotating at a speed of $2500$ revolutions per minute $($rpm$).$ The liquid mixture contains particles with a mass of $0\mathrm{.}002kg$ each. Assume that the centrifuge operates in a gravitational field of $9\mathrm{.}8\frac{m}{s^2}$ and the viscosity of the fluid is $0\mathrm{.}002Pa*s.$

Determine:

a$)$ The angular velocity of the centrifuge in radians per second

b$)$ Centrifugal force acts on a single particle

c$)$ Calculate the sedimentation rate for the given particle

d$)$ Discuss two ways in which the separation efficiency of the centrifuge could be

optimized. Consider factors such as rotor speed, particle size, and the properties of the liquid medium.