A drainage pipe beneath a dam has become clogged with sand whose coefficient of permeability is

$10$m$/$day$.$ It has been observed that the flow through the pipe is $0\mathrm{.}15$ m$3$

$/$day when the difference of

water levels on upstream and downstream is $20$ m$.$ If the cross$-$sectional area of the pipe was

$200$ cm$2$

$,$ what length of the pipe was filled with sand?