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Scholar
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Date Posted: 7/24/2008 2:06:14 AM  Status: Live
help will rate...thermo
Course Textbook Chapter Problem
Thermodynamics Fundamentals of Engineering Thermodynamics (5th) by Moran, Shapiro 4 N/A
Question Details:

Problem 4.007
A water storage tank initially contains 100,000 gal of water. The average daily usage is 13935 gal. If water is added to the
tank at an average rate of 5000[exp(–t/20)] gallons per day, where t is time in days, for how many days will the tank contain
water?

days
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Oracle
Karma Points: 15,230
Date Posted: 7/26/2008 1:02:14 AM  Status: Live
Asker's Rating: Helpful   
Response:
let y(t) be gallons after t days
dy(t)/dt = 5000e-t/20 - 13935
with initial condition y(0) = 100,000
y(t) = ∫ (5000e-t/20 - 13935) dt
= -100,000e-t/20 - 13935t + C
y(0) = 100,000 = -100,000 + C
so C = 200,000
y(t) = 100,000(2 - e-t/20) - 13935t = 10,000[20(2 - e-t/20) - 1.3935t]
let y(t) = 0
20(2 - e-t/20) = 1.3935t
solve it and get t = 7.4 days



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