brittany.hemicker
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- Joined
- Apr 20, 2015
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Hello! I am stuck on a problem in my Calc class. The problem reads: "In many parts of the world, the water for sprinkler systems in large hotels and hospitals is supplied by gravity from cylindrical tanks on or near the roofs of the buildings. Suppose such a tank has radius 10 ft and the diameter of the outlet is 2.5 inches. An engineer has to guarantee that the water pressure will be at least 2160lb/ft^2 for 10 minutes. What height should the engineer specify for the tank? Use the fact that the water pressure at a depth of d feet is p=62.5d.
Here's what I have so far: by solving for the depth, I know d must be 34.56 feet. I also know that means my final answer for height will be greater than that. I'm thinking I need to find dv/dt using Torricelli's law and then find dh/dt to bridge the gap. Once I find dh/dt, I know that I have to set it equal to something else to find the constant value which would be my height. I'm just not sure how to set up the equation.
Here's what I have so far: by solving for the depth, I know d must be 34.56 feet. I also know that means my final answer for height will be greater than that. I'm thinking I need to find dv/dt using Torricelli's law and then find dh/dt to bridge the gap. Once I find dh/dt, I know that I have to set it equal to something else to find the constant value which would be my height. I'm just not sure how to set up the equation.