Water Pressure in a Residential Building: For many years the tallest building in the state of Oklahoma was the City Place Tower in Oklahoma City. The City Place Tower was completed in $1931$ and is $33$ floors tall $(330ft,$ or $101m)$ at a total cost of $3$ million USD. For context, this is about $20\%$ of the height of the tallest building in the US$,$ which is now the One World Trade Center in New York City $($standing at $1776\text{'}).$

Recently, the top seven floors of the City Place Tower were converted into luxury condominiums. One challenge associated with the management of such a tall building is meeting the static water pressure requirements on the top floor. You can assume that the water pressure there should be at least $40\mathrm{.}0(276$kPa$)$ to satisfy consumer requirements. The water main is buried $10\mathrm{.}0m$ below ground along Park Avenue.

Assuming that no shaft work is performed by intermediate pumps between the water main and the shower head, and that frictional energy losses can be neglected, calculate the water pressure in the water main inlet necessary to achieve $40$ water at the shower head outlet. The volumetric flow rate is $0\mathrm{.}160\frac{L}{s}.$ The density of water is $1000k\frac{g}{m^3}.$ The water main diameter is $0\mathrm{.}400m.$ You can model the shower head as a single outlet with a diameter of $1\mathrm{.}00cm.$