$893$ A geothermal district heating system involves the

transport of geothermal water at $110$C from a geothermal

well to a city at about the same elevation for a distance of

$12$ km at a rate of $1\mathrm{.}5$ m$3/$s in $60-$cm$-$diameter stainless$-$steel

pipes. The fluid pressures at the wellhead and the arrival point

in the city are to be the same. The minor losses are negligi$-$

ble because of the large length$-$to$-$diameter ratio and the rela$-$

tively small number of components that cause minor losses.

$($a$)$ Assuming the pump$$motor efficiency to be $80$ percent,

determine the electric power consumption of the system for

pumping. Would you recommend the use of a single large

pump or several smaller pumps of the same total pumping

power scattered along the pipeline? Explain. $($b$)$ Determine

the daily cost of power consumption of the system if the unit

cost of electricity is $$0\mathrm{.}06/$kWh$.($c$)$ The temperature of geothermal

water is estimated to drop $0\mathrm{.}5$C during this long

flow. Determine if the frictional heating during flow can

make up for this drop in temperature.

$894$ Repeat Prob. $893$ for cast iron pipes of the same

diameter.

Notes: Answer $8-94$ only. Exlude Part C$.$

Dynamic viscosity of geothermal water $=0\mathrm{.}225$ x$10^-3$ kg$/$ms

Density of geothermal water $=950\mathrm{.}6$ kg$/$m$^3$