15. Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water drains out at a rate of cubic feet per second. Note: The volume of a cylinder is V = TTrh. A. Find the volume Vs of the water remaining in the small tank as a function of time. B. How long does it take for the small tank to completely empty? C. Let z be the depth of the water in the large tank, which is initially empty. Compute dt D. What fraction of the total amount of water is in the large tank at time t = 6?
15. Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water drains out at a rate of cubic feet per second. Note: The volume of a cylinder is V = TTrh. A. Find the volume Vs of the water remaining in the small tank as a function of time. B. How long does it take for the small tank to completely empty? C. Let z be the depth of the water in the large tank, which is initially empty. Compute dt D. What fraction of the total amount of water is in the large tank at time t = 6?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:15. Water is draining from a small cylindrical tank into a larger one below it. The small
cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a
radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water
drains out at a rate of cubic feet per second. Note: The volume of a cylinder is V = ?h.
A. Find the volume Vs of the water remaining in the small tank as a function of
time.
B. How long does it take for the small tank to completely empty?
C. Let z be the depth of the water in the large tank, which is initially empty. Compute .
dz
D. What fraction of the total amount of water is in the large tank at time t = 6?
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