P$6\mathrm{.}85$ For the system in Prob. P$6\mathrm{.}53,$ a pump, which delivers $\backslash (15,000\backslash$mathrm$\{$~W$\}\backslash )$ to the water, is used at night to refill the upper reservoir. The pipe diameter is increased from $12$ cm to provide more flow. If the resultant flow rate is $\backslash (90\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$h$\}\backslash ),$ estimate the new pipe size. $($the known answer is $0\mathrm{.}188$m; explain process$)$