A water storage tank has the shape of a cylinder with diameter d ft. It is mounted so that the circular cross- sections are vertical. Assume the depth of the water is h ft: the following figure shows the tank cross- section whose center placed at the origin of ay-plane: h If the tank length is L, what would be the volume of water in tank? I SV Hint: The required volume is given by L y d TIL (21 TL 724 TL √(E)* #² [V (E) ² - 2² 2 2h-d (d-2h) /h(d-h) √/hid = h) + i sin 1 (2√/2(6-4) ) + 16-21) (96-A)]) -1 d 4 None (2h-d) √/h(d - h) + z [(2h - d) √/h (d-h) + f sin ¹ (2√/412-43) 414-2020 /10-27 2√√/h(d-h) (d-2h) /h(d-h) L -1 + 2h-d 2 √h(d-h) + (d-2h) /h(d-h) (d-2h)√/h(d-h) 8 TZ [-sin-1 (2√AG-A) 4+4 d TL (2h-d) √h(d-h) + HL. (2h I x² + (n − 4 ) (h (d-2h)√/h(d-h) 2 2√/h(d-h) dx
A water storage tank has the shape of a cylinder with diameter d ft. It is mounted so that the circular cross- sections are vertical. Assume the depth of the water is h ft: the following figure shows the tank cross- section whose center placed at the origin of ay-plane: h If the tank length is L, what would be the volume of water in tank? I SV Hint: The required volume is given by L y d TIL (21 TL 724 TL √(E)* #² [V (E) ² - 2² 2 2h-d (d-2h) /h(d-h) √/hid = h) + i sin 1 (2√/2(6-4) ) + 16-21) (96-A)]) -1 d 4 None (2h-d) √/h(d - h) + z [(2h - d) √/h (d-h) + f sin ¹ (2√/412-43) 414-2020 /10-27 2√√/h(d-h) (d-2h) /h(d-h) L -1 + 2h-d 2 √h(d-h) + (d-2h) /h(d-h) (d-2h)√/h(d-h) 8 TZ [-sin-1 (2√AG-A) 4+4 d TL (2h-d) √h(d-h) + HL. (2h I x² + (n − 4 ) (h (d-2h)√/h(d-h) 2 2√/h(d-h) dx
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![A water storage tank has the shape of a cylinder with
diameter d ft. It is mounted so that the circular cross-
sections are vertical. Assume the depth of the water
is h ft: the following figure shows the tank cross-
section whose center placed at the origin of
xy-plane:
h
y
If the tank length is L, what would be the volume of
water in tank?
d
Hint: The required volume is given by
I SV
L
2h-d
이어서
"V(E)* #² [V (E) ² - 10²
2
TIL (21
TL (2h-d) √h(d – h) +
√/hi(d_h) + f sin + (2√(1-x)) + 16-20/M-)
-1
(d-2h)√/h(d-h)
d
4
None
72. [244
2h-d
TL
2 √h(d-h) +
(d-2h) /h(d-h)
I
z [(2h - d) √/h (d = h) + f sin ¹ (2√/12 -43) 4 14 2012 (107)
2√√/h(d-h)
-1
(d-2h) /h(d-h)
L
+
2
(d-2h)√/h(d-h)
8
√/h(d-h)
(d-2h) /h(d-h)
972 [ain 1 (23/AMG4-A1) 4+ (04-2014/408-10]
d
x² + (h
TL [(2h - d.) /h(d = h) + fatin-¹ (2/6d-43)]
2√/h(d-h)
(2h-d)
9)]
dx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff91a3c08-778f-421e-b4f6-916dbf61d548%2Fc9457277-e4b2-49c9-bbc7-3c0e417994bf%2Fhgvlu2mo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A water storage tank has the shape of a cylinder with
diameter d ft. It is mounted so that the circular cross-
sections are vertical. Assume the depth of the water
is h ft: the following figure shows the tank cross-
section whose center placed at the origin of
xy-plane:
h
y
If the tank length is L, what would be the volume of
water in tank?
d
Hint: The required volume is given by
I SV
L
2h-d
이어서
"V(E)* #² [V (E) ² - 10²
2
TIL (21
TL (2h-d) √h(d – h) +
√/hi(d_h) + f sin + (2√(1-x)) + 16-20/M-)
-1
(d-2h)√/h(d-h)
d
4
None
72. [244
2h-d
TL
2 √h(d-h) +
(d-2h) /h(d-h)
I
z [(2h - d) √/h (d = h) + f sin ¹ (2√/12 -43) 4 14 2012 (107)
2√√/h(d-h)
-1
(d-2h) /h(d-h)
L
+
2
(d-2h)√/h(d-h)
8
√/h(d-h)
(d-2h) /h(d-h)
972 [ain 1 (23/AMG4-A1) 4+ (04-2014/408-10]
d
x² + (h
TL [(2h - d.) /h(d = h) + fatin-¹ (2/6d-43)]
2√/h(d-h)
(2h-d)
9)]
dx
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