Answer the problems below. Work neatly and show all steps to the solution to receive full credit. Include diagrams where appropriate. Express all answers to $3$ significant figures. Always include units.

$(50$ points$)$ The Hoover Dam retains water $400$ feet above turbines used to generate hydroelectric power. The efficiency of the turbines in converting the potential energy of the water stored in the reservoir to electrical energy is $70\%.$ At full capacity the dam produces $1,000,000kW*h$ of energy per day. What is the volumetric flow rate in liters per hour of water flowing through the turbines at the Hoover Dam? How much coal must be burned in a conventional coal fired power plant to produce the same energy if the coal$-$fired plant efficiency is $40\%$ and the heating value of coal is $12,000$ BTU per pound of coal?