24. DısCHARGING Water FROM A TANK A container that has a constant cross section A is filled with water to height H. (See the accompanying figure.) The water is discharged through an opening of cross section B at the base of the container. By using Torricelli's Law, it can be shown that the height h of the water at time t satisfies the initial- value problem dh B / 2gh A h(0) = H dt a. Find an expression for h. b. Find the time T it takes for the tank to empty. c. Find T if A = 4 (ft²), B = 1 (in.²), H = 16 (ft), and t = 32 (ft/sec²). A ft H ft B in.?
24. DısCHARGING Water FROM A TANK A container that has a constant cross section A is filled with water to height H. (See the accompanying figure.) The water is discharged through an opening of cross section B at the base of the container. By using Torricelli's Law, it can be shown that the height h of the water at time t satisfies the initial- value problem dh B / 2gh A h(0) = H dt a. Find an expression for h. b. Find the time T it takes for the tank to empty. c. Find T if A = 4 (ft²), B = 1 (in.²), H = 16 (ft), and t = 32 (ft/sec²). A ft H ft B in.?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![24. DısCHARGING Water FROM A TANK A container that has a
constant cross section A is filled with water to height H.
(See the accompanying figure.) The water is discharged
through an opening of cross section B at the base of the
container. By using Torricelli's Law, it can be shown that
the height h of the water at time t satisfies the initial-
value problem
dh
В
V 2gh
A
h(0) = H
dt
a. Find an expression for h.
b. Find the time T it takes for the tank to empty.
c. Find T if A = 4 (ft²), B = 1 (in.²), H = 16 (ft), and
t = 32 (ft/sec²).
A ft
H ft
B in.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21189ddd-66fa-4fc4-bc34-ed1bb6589050%2F17be132c-12a0-4b1e-8813-ef952eb34c48%2Fm1wb1ik_processed.png&w=3840&q=75)
Transcribed Image Text:24. DısCHARGING Water FROM A TANK A container that has a
constant cross section A is filled with water to height H.
(See the accompanying figure.) The water is discharged
through an opening of cross section B at the base of the
container. By using Torricelli's Law, it can be shown that
the height h of the water at time t satisfies the initial-
value problem
dh
В
V 2gh
A
h(0) = H
dt
a. Find an expression for h.
b. Find the time T it takes for the tank to empty.
c. Find T if A = 4 (ft²), B = 1 (in.²), H = 16 (ft), and
t = 32 (ft/sec²).
A ft
H ft
B in.
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