The plumbing system in a house carries water ($\rho = 1000\:kg/m^3$) from the pipes in the basement up to a faucet on the 3rd floor, $10.7\:m$ above the basement. The water in the basement pipe flows with a pressure of $6.00\times 10^5\:Pa$ and a flow speed of $1.50\:m/s$. The faucet on the 3rd floor has a water pressure of $2.75\times 10^5\:Pa$.

What is the ratio of the diameter of the basement pipe to the diameter of the 3rd floor pipe, $d_0/d_3$?