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In the movie "The Drowning Pool", private detective Lew Harper (payed by Paul Newman) is trapped by the bad guy in a room containing a swimming pool.
This challenge is solved. See the solution below...
- The room may be considered rectangular, 5 meters wide by 15 meters long, with a skylight window 10 meters above the floor.
- There is a single entry to the room, reached by a stairway: a locked 2-m hight by 1-m wide door, whose bottom is 1 meter above the floor.
- Harper knows that his enemy will return in eight hours and decides he can escape by filling the room with water and floating up to the skylight.
- He plugs the drain with his clothes, turns on the water valves, and prepares to put his plan into action.
Assume the water enters the room at about five times the rate at which it enters an average bathtub and that the door can withstand a maximum force of 4500 newtons. Estimate whether the door will break before the room fills and whether Harper has time to escape if the door holds. State any Assumptions you make.
Will Paul Newman make it!?
Challenge Solution:
Lets take a look at the ChEnected challenge problem for this past month, September 2010. The problem asked if a man could escape a room through a sky light by flooding that room with water. His plan hinged on the structural integrity of a door.
- The room is 5 meters wide 15 meters long and 10 meters tall. The door is 2 meters tall and 1 meter wide and is at the top of a 1 meter tall flight of stairs. The door can only withstand 4500 newtons of force before breaking.
- To see if the plan could work lets see what force the door would be under if the room was filled with water. To calculate this we will use the fluid head height equation.
- Pressure (pa) = density (kg/m3) * force of gravity (m/s2) * height (m)
Height in this case is how far under water the door is. When the room is completely filled the middle of the door will be 8 meters under water (by using the middle we won't have to average the forces over the doors height later on)
- 1000 kg/m3 * 9.81 m/s2 * 8 m = 78480 pa
- pa = N / m2 So by multiplying by the doors surface area, 2m2, we can find the force on the door.
- 78480 pa * 2 m2 = 156960 N
This value is much greater than the 4500 Newtons the door can withstand. It will break long before the room fills with water. Paul Newman will not be able to reach the sky light, but he will be able to escape the room when the door bursts.
Thanks to everyone who submitted an answer! Be sure to participate in next month's challenge. If you have an Idea for a ChEnected challenge problem we would love to hear it! Have a challenge of your own for the community? Let us know.