A cylindrical tank in a vertical position with a diameter D = 2 m and a height h = 10 m is initially filled with water. At the base of the tank, there is an orifice with a diameter d = 2 cm which was opened at a time t in such a way as to allow the water to flow under the effect of gravity. Find the function h (t) of water in the tank at time t. Find the times when the height is half, quarter of the initial height, as well as the time required to empty the tank. Use the following differential equation to solve the problem. π R² dh dt k B√2gh
A cylindrical tank in a vertical position with a diameter D = 2 m and a height h = 10 m is initially filled with water. At the base of the tank, there is an orifice with a diameter d = 2 cm which was opened at a time t in such a way as to allow the water to flow under the effect of gravity. Find the function h (t) of water in the tank at time t. Find the times when the height is half, quarter of the initial height, as well as the time required to empty the tank. Use the following differential equation to solve the problem. π R² dh dt k B√2gh
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.1: Quadratic Functions And Models
Problem 56E: When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream...
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A cylindrical tank in a vertical position with a diameter D = 2 m and a height h 10 m is initially filled
with water. At the base of the tank, there is an orifice with a diameter d = 2 cm which was opened at a
time t in such a way as to allow the water to flow under the effect of gravity. Find the function h (t) of
water in the tank at time t. Find the times when the height is half, quarter of the initial height, as well as
the time required to empty the tank. Use the following differential equation to solve the problem.
dh
πR²
dt
Where B is the surface of the orifice.
=-k B√√2gh
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