You are in charge of the construction site of a new dam. Extremely heavy rainfall starts and Bureau of Meteorology hydrologists tell you that beginning at about 8 AM, 2 GL per hour (2 x 10^6 meters^3 per hour) will flow into the dam. The lake behind the dam has approximately vertical walls and a surface area of 1 x 10^6 meters^. At 8 AM, you measure the water level behind the dam: it is 6.5 m below the top of the incomplete dam, and if it overflows, it could sweep away construction equipment on the top. Water from the lake is draining freely and steadily through the dam’s diversion tunnel. The short, horizontal diversion tunnel is 3 m in diameter, has its centerline 40 m below the top of the incomplete dam, and exits to atmospheric pressure. How much time have you got to move equipment from the top before it overflows?
[Hint: First, draw a diagram, then derive a formula for the time the water takes to reach a given height, then put in the numbers.]