c$)$ A liquid fuel with a density of $863$ kg m $-3$ and a flow rate of $0\mathrm{.}7$ m$3$ s$-1$ is to

be delivered by the operating pipeline of $10,882$ m long. The annual

charges $($interest on capital, maintenance and depreciation$)$ on the pipeline

are $100$ D$2$ per m length, where D is the pipe diameter in metres. The

design engineer overestimated the operating pipeline diameter by $74\%$

$($from its optimum value$).$ What is the extra total annual cost linked to this

overestimation?

$$ Darcy friction factor for the flow conditions in the pipe is $8$x$10-3.$

$$ Pipe length given is an equivalent length allowing for all fittings.

$$ Pumping efficiency is $76\%.$

$$ Cost of electricity for pumping is $400$ per kW per year.

$$ g $=9\mathrm{.}81$ m s $-2.$

$$ The pipe is horizontal.

d$)$ The pipework system of a process is $750$ m long, $0\mathrm{.}15$ m diameter and

includes $3$ valves and $4$ bends with the following characteristic:

Q $($m $3$ s$-1)$ H $($m fluid$)$

$0\mathrm{.}20032\mathrm{.}000$

$0\mathrm{.}22535\mathrm{.}188$

$0\mathrm{.}25038\mathrm{.}750$

$0\mathrm{.}27542\mathrm{.}688$

$0\mathrm{.}30047\mathrm{.}000$

$0\mathrm{.}32551\mathrm{.}688$

$0\mathrm{.}35056\mathrm{.}750$

utilising a centrifugal pump with impeller diameter $0\mathrm{.}4$ m and running at

$1450$ rev min$-1$ for with following characteristics:

C H $=8-2$ CQ $-210$ CQ$^2$

where C H is the head coefficient and CQ is the flow coefficient.

i$)$ Determine the flow rate delivered and the pump operating head.

ii$)$ What would be the flow rate through the system if two such pumps were

connected firstly in series and secondly in parallel?

e$)$ The pump in the Figure $2\mathrm{.}2$ is used to move water at $25$C$.$ Given the

information below what is the maximum elevation, z$1,$ of the pump to avoid

cavitation?

$$ The NPSH required for this pump is $3\mathrm{.}5$ m$.$

$$ Diameter of the pipe is $30$ mm$.$

$$ The flow rate is $1$ L s$-1.$

$$ The total losses are equal to $10$ velocity heads.

$$ Atmospheric pressure, Patm $,$ is $101325$ Pa$.$

$$ Vapour pressure of water at $25$C$,$ PV $,$ is $3169$ Pa$.$

$$ The density of water is $1000$ kg m$-3.$

$$ The acceleration due to gravity, g$,$ is $9\mathrm{.}81$ m s $-2.$

Figure $2\mathrm{.}2$ pump and tank diagram

$3.($a$)$ Describe and explain what information is needed to design an adsorption

process, for example recovering an antibiotic from solution in a bioreactor.

Include a comment on key features of an adsorbent make it desirable for

this process.

$($b$)$ A glass bottle containing a dilute solution of compound $$Z$$ is sealed using

a rubber inverted square base pyramidal frustum of $80$ mm height $($see

Figure $3\mathrm{.}1).$ Over time $$Z$$ will diffuse out of the bottle through the rubber.

The relationship between the distance from the top of the stopper $$y$$ and

the distance $$x$$ is given by:

x $=(($h $+$ a$)$ y$)/$tan $\backslash$theta

where $$x$$ is half the width of the frustrum at any particular height, $$a$$ is an

unknown constant and $$h$$ is the height of the stopper.

$($i$)$ Calculate the rate of diffusion given the information in fig $3\mathrm{.}1$ and

the data section for this question.

$($ii$)$ What key assumptions have you made to solve this problem?

$[5\%]$

DATA for part $($b$)$:

x$1=5$ mm

x$2=30$ mm

$\backslash$theta $=73\backslash$deg

D $=0\mathrm{.}5\backslash$times $10-9$ m $2$ s $-1,$ diffusivity of Z in rubber

C $1=1\mathrm{.}5\backslash$times $10-3$ kmol m$-3,$ concentration of Z in the rubber at y$=$Y$1$

C $2=0$ kmol m$-3,$ concentration of Z in the rubber at y$=$Y$2$

Figure $3\mathrm{.}1$: $3$D view of rubber stopper $($left$)2$D cross$-$section $($right$)$

$($c$)$ A packed bed contains spheres of $15$ mm diameter. The spheres have

$3$ mm $2$ surface per $1$ mm$3$ of bed. Pure liquid is passed through the bed at

$35$ mm s$-1.$ After passing through $1500$ mm of the bed it is $75\%$ saturated.

State the mass balance for this situation and then calculate the initial local

mass transfer coefficient in the column.

$($d$)$ Sketch a fully labelled diagram depicting the concentration profiles of a

diffusing species in the $2-$film theory approximation of the interface

between a gas and a liquid. Briefly state the key points of the model in

bullet point form