The area of faucet is calculated below:
\(\begin{array}{c}A = \frac{\pi }{4}{d^2}\\ = \frac{\pi }{4}{\left( {1.85\;{\rm{cm}} \times \frac{{{{10}^{ - 2}}\;{\rm{m}}}}{{1\;{\rm{cm}}}}} \right)^2}\\ = 2.69 \times {10^{ - 4}}\;{{\rm{m}}^2}\end{array}\)
The velocity at faucet is calculated below:
\(\begin{array}{c}v = \sqrt {2gh} \\ = \sqrt {2\left( {9.81\;{\rm{m/}}{{\rm{s}}^2}} \right)\left( {12.0\;{\rm{m}}} \right)} \\ = 15.34\;{\rm{m/s}}\end{array}\)
Here, g is the gravitational acceleration.
The volume rate of flow water from faucet is calculated below:
\(\begin{array}{c}\dot V = Av\\ = \left( {2.69 \times {{10}^{ - 4}}\;{{\rm{m}}^2}} \right)\left( {15.34\;{\rm{m/s}}} \right)\\ = 4.12 \times {10^{ - 3}}\;{{\rm{m}}^3}{\rm{/s}}\end{array}\)
Hence, the volume rate of flow water from faucet is \(4.12 \times {10^{ - 3}}\;{{\rm{m}}^3}{\rm{/s}}\).