Liquid water $($v $=0\mathrm{.}001$ m$3/$kg$,$ C $=4\mathrm{.}2$ kJ$/$kgK$)$ enters an adiabatic piping system at $15$C at a rate of $5$ kg$/$s$.$ If the water temperature rises by $0\mathrm{.}5$C during the flow due to friction, the rate of entropy generation in the pipe is most closely

A$.$

$22$ W$/$K

B$.$

$36$ W$/$K

C$.$

$685$ W$/$K

D$.$

$920$ W$/$K

E$.$

$8370$ W$/$K

F$.$

none of the above