A large container made to hold water has the equation z = 8 (x² + y²) 7/2 (The z-axis points up.) (a) Find a formula for V (z), the volume of water in the container when its depth is z. ANSWER: V(z) = (b) Suppose that the container is filled to a depth H > 0. At a certain instant, a hole develops at the origin and water starts to drain out. This makes the water depth za decreasing function of time; the water depth has dropped to H/2 exactly 120 minutes after draining begins. Find the first time when all the water is gone; call this T. ANSWER: T = Background: According to Bernoulli's Law, the instantaneous rate of volume loss from a container like ours is proportional to the square root of the water depth.
A large container made to hold water has the equation z = 8 (x² + y²) 7/2 (The z-axis points up.) (a) Find a formula for V (z), the volume of water in the container when its depth is z. ANSWER: V(z) = (b) Suppose that the container is filled to a depth H > 0. At a certain instant, a hole develops at the origin and water starts to drain out. This makes the water depth za decreasing function of time; the water depth has dropped to H/2 exactly 120 minutes after draining begins. Find the first time when all the water is gone; call this T. ANSWER: T = Background: According to Bernoulli's Law, the instantaneous rate of volume loss from a container like ours is proportional to the square root of the water depth.
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 large container made to hold water has the equation
= 8(x² + y²) 7/².
2=
(The z-axis points up.)
(a) Find a formula for V(z), the volume of water in the container when its depth is z.
ANSWER: V(2) =
(b) Suppose that the container is filled to a depth H > 0. At a certain instant, a hole develops at the origin and water
starts to drain out. This makes the water depth za decreasing function of time; the water depth has dropped to H/2
exactly 120 minutes after draining begins. Find the first time when all the water is gone; call this T.
ANSWER: T=
Background: According to Bernoulli's Law, the instantaneous rate of volume loss from a container like ours is
proportional to the square root of the water depth.
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