The clepsydra, or water clock, was a device that the ancient Egyptians, Greeks, Romans, and Chinese used to measure the passage of time by observing the change in the height of water that was permitted to flow out of a small hole in the bottom of a container or tank. (a) Suppose a tank is made of glass and has the shape of a right-circular cylinder of radius 1 ft. Assume that h(0) = 2 ft corresponds to water filled to the top of the tank, a hole in the bottom is circular with radius = 1/32 in., g= 32 ft/s2, and c= 0.6. Find the height h(t) of the water. (b) For the tank in part (a), how far up from its bottom should a mark be made on its side, as shown in the figure below, that corresponds to the passage of one hour? Next determine where to place the marks corresponding to the passage of 2 hr, 3 hr, .. ., 12 hr. Explain why these marks are not evenly spaced. 1 hour 2 hours
The clepsydra, or water clock, was a device that the ancient Egyptians, Greeks, Romans, and Chinese used to measure the passage of time by observing the change in the height of water that was permitted to flow out of a small hole in the bottom of a container or tank. (a) Suppose a tank is made of glass and has the shape of a right-circular cylinder of radius 1 ft. Assume that h(0) = 2 ft corresponds to water filled to the top of the tank, a hole in the bottom is circular with radius = 1/32 in., g= 32 ft/s2, and c= 0.6. Find the height h(t) of the water. (b) For the tank in part (a), how far up from its bottom should a mark be made on its side, as shown in the figure below, that corresponds to the passage of one hour? Next determine where to place the marks corresponding to the passage of 2 hr, 3 hr, .. ., 12 hr. Explain why these marks are not evenly spaced. 1 hour 2 hours
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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Transcribed Image Text:The clepsydra, or water clock, was a device that the ancient
Egyptians, Greeks, Romans, and Chinese used to measure the
passage of time by observing the change in the height of water
that was permitted to flow out of a small hole in the bottom of a
container or tank.
(a) Suppose a tank is made of glass and has the shape of a
right-circular cylinder of radius 1 ft. Assume that h(0) = 2 ft
%3D
corresponds to water filled to the top of the tank, a hole in the
bottom is circular with radius =
1/32 in., g= 32 ft/s2, and c= 0.6.
Find the height h(t) of the water.
(b) For the tank in part (a), how far up from its bottom should a
mark be made on its side, as shown in the figure below, that
corresponds to the passage of one hour? Next determine where
to place the marks corresponding to the passage of 2 hr, 3 hr, ..
12 hr. Explain why these marks are not evenly spaced.
1 hour
2 hours
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