A hemi-spherical tank of radius 2 m is initially full of water and has an outlet of 12 cm² cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law v(t) = 0.6 √2gh(t), where v(t) and h(t) are, respectively, the velocity of the flow through the outlet and the height of water level above the outlet at time t, and g is the acceleration due to gravity. Find the time it takes o empty the tank.
A hemi-spherical tank of radius 2 m is initially full of water and has an outlet of 12 cm² cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law v(t) = 0.6 √2gh(t), where v(t) and h(t) are, respectively, the velocity of the flow through the outlet and the height of water level above the outlet at time t, and g is the acceleration due to gravity. Find the time it takes o empty the tank.
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:A hemi-spherical tank of radius 2 m is initially full of water
and has an outlet of 12 cm² cross-sectional area at the bottom.
The outlet is opened at some instant. The flow through the
outlet is according to the law v(t) = 0.6 √√2gh(t), where v(t)
and h(t) are, respectively, the velocity of the flow through the
outlet and the height of water level above the outlet at time t,
and g is the acceleration due to gravity. Find the time it takes
to empty the tank.
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