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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. 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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text:= 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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